env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ⊗, the rules are as follows:
when x is less than y, x ⊗ y = x + x + x - y ** x;
otherwise, x ⊗ y = 2 + y + x + 4 + 2.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = (y * x + x) * y.
and ◇, the rules are as follows:
when x is even, x ◇ y = x + y + y + x / y;
otherwise, x ◇ y = x - y ⊙ y.
The precedence of operations: ⊙ = ◇ > ** = ⊗ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ⊗ 10 ◇ 8 ⊙ 5
Please fill your final answer in \boxed{}. | {
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"expression": "6 ⊗ 10 ◇ 8 ⊙ 5",
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"seed": 41136671,
"simplified_expr": "( 2 + (( (5 * (( 10 + 8 + 8 + 10 / 8)) + (( 10 + 8 + 8 + 10 / 8))) * 5)) + 6 + 4 + 2)",
"solutions_count": null,
"symbol_definitions": {
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"⊗": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " x + x + x - y ** x"
}
],
"default_operation": " 2 + y + x + 4 + 2",
"precedence": 3
},
"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " (y * x + x) * y",
"precedence": 5
},
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " x + y + y + x / y"
}
],
"default_operation": " x - y ⊙ y",
"precedence": 5
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "06069d0e-20d7-4845-bdd7-8bdce0406f45"
},
"question": "Define ⊗, the rules are as follows:\nwhen x is less than y, x ⊗ y = x + x + x - y ** x;\notherwise, x ⊗ y = 2 + y + x + 4 + 2.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = (y * x + x) * y.\nand ◇, the rules are as follows:\nwhen x is even, x ◇ y = x + y + y + x / y;\notherwise, x ◇ y = x - y ⊙ y.\nThe precedence of operations: ⊙ = ◇ > ** = ⊗ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 ⊗ 10 ◇ 8 ⊙ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "6 ⊗ 10 ◇ 8 ⊙ 5",
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"seed": 41136671,
"simplified_expr": "( 2 + (( (5 * (( 10 + 8 + 8 + 10 / 8)) + (( 10 + 8 + 8 + 10 / 8))) * 5)) + 6 + 4 + 2)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [
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"condition": "x小于y",
"operation": " x + x + x - y ** x"
}
],
"default_operation": " 2 + y + x + 4 + 2",
"precedence": 3
},
"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " (y * x + x) * y",
"precedence": 5
},
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " x + y + y + x / y"
}
],
"default_operation": " x - y ⊙ y",
"precedence": 5
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "06069d0e-20d7-4845-bdd7-8bdce0406f45"
},
"seed": 41136671,
"task_id": 241136671,
"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = 4 / y + x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y / x.
and ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = x ** y + y;
otherwise, x ⊗ y = x / x * y.
The precedence of operations: ◎ > ♡ = ⊗ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ⊗ 7 ◎ 6 ♡ 1
Please fill your final answer in \boxed{}. | {
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"gpt_response": "",
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"expression": "8 ⊗ 7 ◎ 6 ♡ 1",
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"seed": 34177791,
"simplified_expr": "( 1 / (( 8 / 8 * (( 4 / 6 + 7)))))",
"solutions_count": null,
"symbol_definitions": {
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"⊗": {
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"default_operation": " x / x * y",
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " 4 / y + x",
"precedence": 5
},
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x",
"precedence": 4
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "1f868ccb-31c2-49fb-a966-929ae76be791"
},
"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = 4 / y + x.\nand ♡, the rules are as follows:\non the real number field, x ♡ y = y / x.\nand ⊗, the rules are as follows:\nwhen x is greater than y, x ⊗ y = x ** y + y;\notherwise, x ⊗ y = x / x * y.\nThe precedence of operations: ◎ > ♡ = ⊗ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 8 ⊗ 7 ◎ 6 ♡ 1\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 7 ◎ 6 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 34177791,
"simplified_expr": "( 1 / (( 8 / 8 * (( 4 / 6 + 7)))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " x ** y + y"
}
],
"default_operation": " x / x * y",
"precedence": 4
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " 4 / y + x",
"precedence": 5
},
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x",
"precedence": 4
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "1f868ccb-31c2-49fb-a966-929ae76be791"
},
"seed": 34177791,
"task_id": 234177791,
"task_type": "operation"
} |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y - x + 2 * y。
和 ☆，规则如下：
实数域上，x ☆ y = x / abs(y) / x。
运算优先级：☆ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◎ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
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"expression": "8 ◎ 8",
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"seed": 67969380,
"simplified_expr": "( 8 - 8 + 2 * 8)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x + 2 * y",
"precedence": 1
},
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x / abs(y) / x",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "7d4cf39d-0055-4bc6-9e85-3b2d96344e3e"
},
"question": "定义 ◎，规则如下：\n实数域上，x ◎ y = y - x + 2 * y。\n和 ☆，规则如下：\n实数域上，x ☆ y = x / abs(y) / x。\n运算优先级：☆ > ** > * = / = % > + = - = ◎。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 ◎ 8\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 8",
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"seed": 67969380,
"simplified_expr": "( 8 - 8 + 2 * 8)",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x + 2 * y",
"precedence": 1
},
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x / abs(y) / x",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "7d4cf39d-0055-4bc6-9e85-3b2d96344e3e"
},
"seed": 67969380,
"task_id": 267969380,
"task_type": "operation"
} |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x * x * y - y。
和 △，规则如下：
当x小于y时，x △ y = x / y + y；
其他情况下，x △ y = y + 5 ○ 1 * x。
和 ☆，规则如下：
实数域上，x ☆ y = x / 4 * 2 ○ x + y。
运算优先级：○ > ** = △ > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ☆ 10 ○ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "297.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 10 ○ 3",
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"seed": 17079367,
"simplified_expr": "((((((1 / 4)) * (( 2 * 2 * 1 - 1)))) + ((((((10 * 10)) * 3)) - 3))))",
"solutions_count": null,
"symbol_definitions": {
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}
],
"default_operation": " y + 5 ○ 1 * x",
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},
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x * x * y - y",
"precedence": 5
},
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x / 4 * 2 ○ x + y",
"precedence": 1
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "f8ada20e-a4af-47bb-84c6-84db7bdf3fa1"
},
"question": "定义 ○，规则如下：\n实数域上，x ○ y = x * x * y - y。\n和 △，规则如下：\n当x小于y时，x △ y = x / y + y；\n其他情况下，x △ y = y + 5 ○ 1 * x。\n和 ☆，规则如下：\n实数域上，x ☆ y = x / 4 * 2 ○ x + y。\n运算优先级：○ > ** = △ > * = / = % > + = - = ☆。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 ☆ 10 ○ 3\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 10 ○ 3",
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"question_sequence": null,
"seed": 17079367,
"simplified_expr": "((((((1 / 4)) * (( 2 * 2 * 1 - 1)))) + ((((((10 * 10)) * 3)) - 3))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
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"△": {
"associativity": "left",
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"operation": " x / y + y"
}
],
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},
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x * x * y - y",
"precedence": 5
},
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x / 4 * 2 ○ x + y",
"precedence": 1
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "f8ada20e-a4af-47bb-84c6-84db7bdf3fa1"
},
"seed": 17079367,
"task_id": 217079367,
"task_type": "operation"
} |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = 3 - y * x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = (5) * y / x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x ⊗ y - x.
The precedence of operations: ◇ > ♢ > ** > * = / = % > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ⊗ 8 ◇ 9 ⊗ 7 ♢ 8
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-829.5",
"difficulty": 1,
"gpt_response": "",
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"num_of_numbers": null,
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 73981804,
"simplified_expr": "( 3 - ((((( 3 - 8 * 7)) - 7))) * (( 3 - (( (5) * 9 / 8)) * 3)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
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"default_operation": " 3 - y * x",
"precedence": 1
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " (5) * y / x",
"precedence": 5
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " x ⊗ y - x",
"precedence": 4
}
},
"target": null,
"total_length": null,
"trace_id": "b55b1cd9-0902-46a3-ab25-15558c495e7d"
},
"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = 3 - y * x.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = (5) * y / x.\nand ♢, the rules are as follows:\non the real number field, x ♢ y = x ⊗ y - x.\nThe precedence of operations: ◇ > ♢ > ** > * = / = % > + = - = ⊗。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ⊗ 8 ◇ 9 ⊗ 7 ♢ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 8 ◇ 9 ⊗ 7 ♢ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 73981804,
"simplified_expr": "( 3 - ((((( 3 - 8 * 7)) - 7))) * (( 3 - (( (5) * 9 / 8)) * 3)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
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"default_operation": " 3 - y * x",
"precedence": 1
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " (5) * y / x",
"precedence": 5
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " x ⊗ y - x",
"precedence": 4
}
},
"target": null,
"total_length": null,
"trace_id": "b55b1cd9-0902-46a3-ab25-15558c495e7d"
},
"seed": 73981804,
"task_id": 273981804,
"task_type": "operation"
} |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x / y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x * y.
The precedence of operations: □ > ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 □ 1 ◇ 2
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
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"expression": "1 □ 1 ◇ 2",
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"seed": 22418263,
"simplified_expr": "( (( 1 / 1)) * 2)",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": {
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"conditions": [],
"default_operation": " x / y",
"precedence": 5
},
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y",
"precedence": 3
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "a64d4e28-b512-472c-8d4f-01f5292b6895"
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"question": "Define □, the rules are as follows:\non the real number field, x □ y = x / y.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = x * y.\nThe precedence of operations: □ > ** = ◇ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 1 □ 1 ◇ 2\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "1 □ 1 ◇ 2",
"fill_length": null,
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y + 4 + x。
和 ◎，规则如下：
实数域上，x ◎ y = y + x * y。
运算优先级：** = ⊗ > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ⊗ 9 ◎ 9 ◎ 8
请将最终答案填入\boxed{}中。 | {
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},
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"seed": 76777023,
"simplified_expr": "( 8 + (( 9 + (( 9 + 4 + 5)) * 9)) * 8)",
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"seed": 76777023,
"task_id": 276777023,
"task_type": "operation"
} |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = 5 ** y - 2 * 1 - x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 6
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | Define △, the rules are as follows:
when x is a multiple of 3, x △ y = y * y + y + x * y;
otherwise, x △ y = x + y * x * y * x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 △ 4 △ 1
Please fill your final answer in \boxed{}. | {
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"seed": 52691174,
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"solutions_count": null,
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},
"metadata": {
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"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [
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"seed": 52691174,
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} |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x - y + y - 5 * x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = (y ⊕ x * x + y * y).
and △, the rules are as follows:
on the real number field, x △ y = y - x / x + y + x.
The precedence of operations: ** = ⊕ = △ > * = / = % > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ♢ 3 △ 10 ⊕ 9
Please fill your final answer in \boxed{}. | {
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"gpt_response": "",
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"expression": "10 ♢ 3 △ 10 ⊕ 9",
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"solutions_count": null,
"symbol_definitions": {
"⊕": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y + y - 5 * x",
"precedence": 3
},
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x / x + y + x",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " (y ⊕ x * x + y * y)",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "5a7c54e3-e9c2-4fa5-affd-28afebd7fd1d"
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"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = x - y + y - 5 * x.\nand ♢, the rules are as follows:\non the real number field, x ♢ y = (y ⊕ x * x + y * y).\nand △, the rules are as follows:\non the real number field, x △ y = y - x / x + y + x.\nThe precedence of operations: ** = ⊕ = △ > * = / = % > + = - = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 ♢ 3 △ 10 ⊕ 9\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "10 ♢ 3 △ 10 ⊕ 9",
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"numbers": null,
"operators": null,
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"seed": 94760708,
"simplified_expr": "(((((( ((((((((((((10 - ((3 / 3)))) + 10)) + 3)) - 9)) + 9)) - ((5 * ((((((10 - ((3 / 3)))) + 10)) + 3)))))) - 10 + 10 - 5 * ((((((((((((10 - ((3 / 3)))) + 10)) + 3)) - 9)) + 9)) - ((5 * ((((((10 - ((3 / 3)))) + 10)) + 3)))))))) * 10)) + ((((((((((((((10 - ((3 / 3)))) + 10)) + 3)) - 9)) + 9)) - ((5 * ((((((10 - ((3 / 3)))) + 10)) + 3)))))) * ((((((((((((10 - ((3 / 3)))) + 10)) + 3)) - 9)) + 9)) - ((5 * ((((((10 - ((3 / 3)))) + 10)) + 3))))))))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y + y - 5 * x",
"precedence": 3
},
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x / x + y + x",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " (y ⊕ x * x + y * y)",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "5a7c54e3-e9c2-4fa5-affd-28afebd7fd1d"
},
"seed": 94760708,
"task_id": 294760708,
"task_type": "operation"
} |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = x * y.
and ♢, the rules are as follows:
when the sum of x and y is odd, x ♢ y = y ♡ y + x / 4;
otherwise, x ♢ y = x + y - x * y.
The precedence of operations: ♢ > ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ♡ 7 % 8 ♢ 4
Please fill your final answer in \boxed{}. | {
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"◎": null,
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"operation": " y ♡ y + x / 4"
}
],
"default_operation": " x + y - x * y",
"precedence": 5
}
},
"target": null,
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"trace_id": "f3a7e902-eb57-400e-b0b5-07933b972670"
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"question": "Define ♡, the rules are as follows:\non the real number field, x ♡ y = x * y.\nand ♢, the rules are as follows:\nwhen the sum of x and y is odd, x ♢ y = y ♡ y + x / 4;\notherwise, x ♢ y = x + y - x * y.\nThe precedence of operations: ♢ > ♡ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 ♡ 7 % 8 ♢ 4\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "9 ♡ 7 % 8 ♢ 4",
"fill_length": null,
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"seed": 68384211,
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"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y",
"precedence": 4
},
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是奇数",
"operation": " y ♡ y + x / 4"
}
],
"default_operation": " x + y - x * y",
"precedence": 5
}
},
"target": null,
"total_length": null,
"trace_id": "f3a7e902-eb57-400e-b0b5-07933b972670"
},
"seed": 68384211,
"task_id": 268384211,
"task_type": "operation"
} |
logic-v2 | Define ○, the rules are as follows:
when x and y are both even, x ○ y = x * y + y;
otherwise, x ○ y = y / x + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y ○ x - y.
The precedence of operations: ** > * = / = % = ○ = ◎ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ◎ 7
Please fill your final answer in \boxed{}. | {
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"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"operation": " x * y + y"
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],
"default_operation": " y / x + y",
"precedence": 2
},
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y ○ x - y",
"precedence": 2
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "d7180a8a-bb20-4837-9e4d-901fca9beb8c"
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"question": "Define ○, the rules are as follows:\nwhen x and y are both even, x ○ y = x * y + y;\notherwise, x ○ y = y / x + y.\nand ◎, the rules are as follows:\non the real number field, x ◎ y = y ○ x - y.\nThe precedence of operations: ** > * = / = % = ○ = ◎ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ◎ 7\nPlease fill your final answer in \\boxed{}."
},
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"operators": null,
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"seed": 69292855,
"simplified_expr": "(((( 2 / 7 + 2)) - 7))",
"solutions_count": null,
"symbol_definitions": {
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"○": {
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},
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y ○ x - y",
"precedence": 2
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logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y / x / x - 3.
and △, the rules are as follows:
on the real number field, x △ y = 3 - y / x * 1.
The precedence of operations: ** > * = / = % = ♡ > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ♡ 4 △ 2 ♡ 8 + 4
Please fill your final answer in \boxed{}. | {
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},
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} |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x + x + 3 * y。
和 ◇，规则如下：
当x等于y时，x ◇ y = 4 + x - y + y；
其他情况下，x ◇ y = x □ y * x。
运算优先级：□ > ** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 □ 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 □，规则如下：\n实数域上，x □ y = x + x + 3 * y。\n和 ◇，规则如下：\n当x等于y时，x ◇ y = 4 + x - y + y；\n其他情况下，x ◇ y = x □ y * x。\n运算优先级：□ > ** > * = / = % = ◇ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 □ 4\n请将最终答案填入\\boxed{}中。"
},
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"seed": 90709858,
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"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
when y is a multiple of 3, x ◎ y = y * y - abs(x);
otherwise, x ◎ y = x - y * x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + y - x.
The precedence of operations: ⊕ > ◎ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ◎ 1
Please fill your final answer in \boxed{}. | {
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},
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},
"seed": 16500592,
"task_id": 216500592,
"task_type": "operation"
} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x + y * x - x + x.
and □, the rules are as follows:
when x is greater than y, x □ y = x / x / y * y ☆ x;
otherwise, x □ y = 4 + x * 5 / y - x.
The precedence of operations: ☆ > ** > * = / = % > + = - = □。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 □ 3 ☆ 2
Please fill your final answer in \boxed{}. | {
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
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"♡": null,
"♢": null
},
"target": null,
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = x + y * x - x + x.\nand □, the rules are as follows:\nwhen x is greater than y, x □ y = x / x / y * y ☆ x;\notherwise, x □ y = 4 + x * 5 / y - x.\nThe precedence of operations: ☆ > ** > * = / = % > + = - = □。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 □ 3 ☆ 2\nPlease fill your final answer in \\boxed{}."
},
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"operators": null,
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"seed": 2346609,
"simplified_expr": "((((((10 / 10)) / ((((((3 + ((2 * 3)))) - 3)) + 3)))) * (( ((((((3 + ((2 * 3)))) - 3)) + 3)) + 10 * ((((((3 + ((2 * 3)))) - 3)) + 3)) - ((((((3 + ((2 * 3)))) - 3)) + 3)) + ((((((3 + ((2 * 3)))) - 3)) + 3))))))",
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
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"default_operation": " x + y * x - x + x",
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"♢": null
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"task_type": "operation"
} |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y * y * 5 * (5 - x)。
和 ⊙，规则如下：
当x是5的倍数时，x ⊙ y = x * (x / y + y) ☆ x；
其他情况下，x ⊙ y = y + (5 ** x) ☆ 2 - y。
运算优先级：⊙ > ** > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ☆ 5
请将最终答案填入\boxed{}中。 | {
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"♢": null
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},
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logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * y + (y).
and ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = y ⊕ x ** y;
otherwise, x ◎ y = y ⊕ x.
and ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = (x - y - y);
otherwise, x ⊙ y = y - x ⊕ y.
The precedence of operations: ⊕ = ⊙ > ** > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ⊕ 10 ◎ 6
Please fill your final answer in \boxed{}. | {
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"△": null,
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"○": null,
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"condition": "x和y的和是奇数",
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},
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"seed": 80310554,
"simplified_expr": "(( 6 * ((((10 * 10)) + 10)) + (((((10 * 10)) + 10)))))",
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logic-v2 | Define ◇, the rules are as follows:
when x is less than y, x ◇ y = y - x * y - y;
otherwise, x ◇ y = x - abs(y + y) - y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x - x * y。
和 ⊗，规则如下：
实数域上，x ⊗ y = y + x + x。
运算优先级：⊗ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 □ 8 * 7 ⊗ 6
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ◎，规则如下：
当x等于y时，x ◎ y = y - 2 + 5 - y + x；
其他情况下，x ◎ y = x + y - y / x * 4。
和 □，规则如下：
实数域上，x □ y = 5 / x ◎ y + 2 + y。
运算优先级：◎ > ** > * = / = % = □ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ◎ 3 □ 3 - 8
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | 定义 ▽，规则如下：
当x和y都是奇数时，x ▽ y = y * 3 * x；
其他情况下，x ▽ y = (y ** 5 * x) + x。
运算优先级：** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | Define ◇, the rules are as follows:
when x is equal to y, x ◇ y = 4 + y / 5 - x;
otherwise, x ◇ y = y + 3 - x * y - y.
The precedence of operations: ** > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ◇ 2 / 8 + 1
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y - x * y.
and ○, the rules are as follows:
on the real number field, x ○ y = y * x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x - (y / x).
The precedence of operations: ○ > ** > * = / = % = ⊗ > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ♢ 5 ⊗ 2
Please fill your final answer in \boxed{}. | {
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},
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"seed": 64276759,
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"task_type": "operation"
} |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x - (x + y + y)。
运算优先级：□ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 □ 5
请将最终答案填入\boxed{}中。 | {
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"simplified_expr": "( 8 - (8 + 5 + 5))",
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"symbol_definitions": {
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},
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"♢": null
},
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"trace_id": "c16e95b4-d1aa-4c08-96b2-38fc07320689"
},
"question": "定义 □，规则如下：\n实数域上，x □ y = x - (x + y + y)。\n运算优先级：□ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 □ 5\n请将最终答案填入\\boxed{}中。"
},
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"expression": "8 □ 5",
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"seed": 74020279,
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} |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * y * 1 - y - y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = 1 - y + x - 4 + x.
and □, the rules are as follows:
when y is even, x □ y = x / y + y;
otherwise, x □ y = x * x + y * abs(x - y).
The precedence of operations: ** = □ > * = / = % = ⊕ = ⊙ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ⊕ 5 □ 4
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
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"expression": "6 ⊕ 5 □ 4",
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"seed": 28789618,
"simplified_expr": "( 6 * (( 5 / 4 + 4)) * 1 - (( 5 / 4 + 4)) - (( 5 / 4 + 4)))",
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"symbol_definitions": {
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"conditions": [],
"default_operation": " 1 - y + x - 4 + x",
"precedence": 2
},
"□": {
"associativity": "left",
"conditions": [
{
"condition": "y是偶数",
"operation": " x / y + y"
}
],
"default_operation": " x * x + y * abs(x - y)",
"precedence": 3
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"target": null,
"total_length": null,
"trace_id": "575b59c1-21a6-42da-b0a2-7f225cfb81b0"
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"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = x * y * 1 - y - y.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = 1 - y + x - 4 + x.\nand □, the rules are as follows:\nwhen y is even, x □ y = x / y + y;\notherwise, x □ y = x * x + y * abs(x - y).\nThe precedence of operations: ** = □ > * = / = % = ⊕ = ⊙ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 ⊕ 5 □ 4\nPlease fill your final answer in \\boxed{}."
},
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"expression": "6 ⊕ 5 □ 4",
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"num_of_numbers": null,
"num_symbols": 3,
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"operators": null,
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"seed": 28789618,
"simplified_expr": "( 6 * (( 5 / 4 + 4)) * 1 - (( 5 / 4 + 4)) - (( 5 / 4 + 4)))",
"solutions_count": null,
"symbol_definitions": {
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"conditions": [],
"default_operation": " 1 - y + x - 4 + x",
"precedence": 2
},
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"associativity": "left",
"conditions": [
{
"condition": "y是偶数",
"operation": " x / y + y"
}
],
"default_operation": " x * x + y * abs(x - y)",
"precedence": 3
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "575b59c1-21a6-42da-b0a2-7f225cfb81b0"
},
"seed": 28789618,
"task_id": 228789618,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
when the sum of x and y is odd, x ◇ y = y * y * y - (x);
otherwise, x ◇ y = x * y - x + x.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ◇ 3 % 10 / 3
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
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"expression": "4 ◇ 3 % 10 / 3",
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 30926530,
"simplified_expr": "( 4 * ((((3 % 10)) / 3)) - 4 + 4)",
"solutions_count": null,
"symbol_definitions": {
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"⊙": null,
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"△": null,
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"◇": {
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"conditions": [
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"operation": " y * y * y - (x)"
}
],
"default_operation": " x * y - x + x",
"precedence": 1
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "bb9bc9c7-4396-4bba-a5d4-f5a13e2f695a"
},
"question": "Define ◇, the rules are as follows:\nwhen the sum of x and y is odd, x ◇ y = y * y * y - (x);\notherwise, x ◇ y = x * y - x + x.\nThe precedence of operations: ** > * = / = % > + = - = ◇。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ◇ 3 % 10 / 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"seed": 30926530,
"simplified_expr": "( 4 * ((((3 % 10)) / 3)) - 4 + 4)",
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"conditions": [
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"operation": " y * y * y - (x)"
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"default_operation": " x * y - x + x",
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},
"○": null,
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"trace_id": "bb9bc9c7-4396-4bba-a5d4-f5a13e2f695a"
},
"seed": 30926530,
"task_id": 230926530,
"task_type": "operation"
} |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y - x + x / x * x.
and △, the rules are as follows:
on the real number field, x △ y = y * x + x ♡ y * x.
The precedence of operations: ♡ > ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 % 2 ♡ 3 ♡ 9 △ 3
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"expression": "10 % 2 ♡ 3 ♡ 9 △ 3",
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"seed": 94726843,
"simplified_expr": "(10 % (((((3 * ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2)))))))))) + (((( 3 - ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2)))))))) + ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2)))))))) / ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2)))))))) * ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2)))))))))) * ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2))))))))))))))",
"solutions_count": null,
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"□": null,
"△": {
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"conditions": [],
"default_operation": " y * x + x ♡ y * x",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x + x / x * x",
"precedence": 4
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "d363fa76-e475-4d64-9920-5a6ac05b9015"
},
"question": "Define ♡, the rules are as follows:\non the real number field, x ♡ y = y - x + x / x * x.\nand △, the rules are as follows:\non the real number field, x △ y = y * x + x ♡ y * x.\nThe precedence of operations: ♡ > ** = △ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 % 2 ♡ 3 ♡ 9 △ 3\nPlease fill your final answer in \\boxed{}."
},
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"seed": 94726843,
"simplified_expr": "(10 % (((((3 * ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2)))))))))) + (((( 3 - ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2)))))))) + ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2)))))))) / ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2)))))))) * ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2)))))))))) * ((((9 - ((((3 - 2)) + ((((2 / 2)) * 2)))))) + ((((((((3 - 2)) + ((((2 / 2)) * 2)))) / ((((3 - 2)) + ((((2 / 2)) * 2)))))) * ((((3 - 2)) + ((((2 / 2)) * 2))))))))))))))",
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},
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"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x + x / x * x",
"precedence": 4
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "d363fa76-e475-4d64-9920-5a6ac05b9015"
},
"seed": 94726843,
"task_id": 294726843,
"task_type": "operation"
} |
logic-v2 | Define ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = x + (y - x);
otherwise, x ⊙ y = x * (y * y).
and □, the rules are as follows:
on the real number field, x □ y = 4 - x ⊙ y.
and ⊕, the rules are as follows:
when y is a multiple of 5, x ⊕ y = (5 + x) ⊙ y;
otherwise, x ⊕ y = y □ 3 + x.
The precedence of operations: ⊙ > ** = ⊕ > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ⊙ 5 □ 9 ⊕ 4 ⊙ 2
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "135",
"difficulty": 1,
"gpt_response": "",
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"expression": "3 ⊙ 5 □ 9 ⊕ 4 ⊙ 2",
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"simplified_expr": "((4 - (( ((3 + ((5 - 3)))) + (((((4 - ((((4 * ((2 * 2)))) * ((3 * 3)))))) + 9)) - ((3 + ((5 - 3)))))))))",
"solutions_count": null,
"symbol_definitions": {
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"conditions": [
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"condition": "x和y都是奇数",
"operation": " x + (y - x)"
}
],
"default_operation": " x * (y * y)",
"precedence": 4
},
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " 4 - x ⊙ y",
"precedence": 2
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "349be8de-a4d3-4dc1-a298-560fde943446"
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"question": "Define ⊙, the rules are as follows:\nwhen x and y are both odd, x ⊙ y = x + (y - x);\notherwise, x ⊙ y = x * (y * y).\nand □, the rules are as follows:\non the real number field, x □ y = 4 - x ⊙ y.\nand ⊕, the rules are as follows:\nwhen y is a multiple of 5, x ⊕ y = (5 + x) ⊙ y;\notherwise, x ⊕ y = y □ 3 + x.\nThe precedence of operations: ⊙ > ** = ⊕ > * = / = % = □ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ⊙ 5 □ 9 ⊕ 4 ⊙ 2\nPlease fill your final answer in \\boxed{}."
},
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"solutions_count": null,
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}
],
"default_operation": " x * (y * y)",
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},
"□": {
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"conditions": [],
"default_operation": " 4 - x ⊙ y",
"precedence": 2
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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},
"seed": 63274931,
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} |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x + y + y。
和 ○，规则如下：
当x大于y时，x ○ y = x * y + x + x；
其他情况下，x ○ y = y + x * y * y。
运算优先级：♡ > ** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ○ 7 + 2 ♡ 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ♡，规则如下：\n实数域上，x ♡ y = x + y + y。\n和 ○，规则如下：\n当x大于y时，x ○ y = x * y + x + x；\n其他情况下，x ○ y = y + x * y * y。\n运算优先级：♡ > ** = ○ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 ○ 7 + 2 ♡ 10\n请将最终答案填入\\boxed{}中。"
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logic-v2 | 定义 ♢，规则如下：
当x是奇数时，x ♢ y = x - y * x * x；
其他情况下，x ♢ y = (x + y * y + x)。
和 ⊙，规则如下：
实数域上，x ⊙ y = (y - x * x)。
和 ☆，规则如下：
当y是奇数时，x ☆ y = 1 - x / abs(y)；
其他情况下，x ☆ y = y - x * y - y。
运算优先级：⊙ > ** = ☆ > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ☆ 4 ♢ 6
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = (x * y + 1) + 3 - x。
和 □，规则如下：
当x是奇数时，x □ y = x + y ◎ y；
其他情况下，x □ y = x - y ** y - x + x。
运算优先级：□ > ◎ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◎ 8 □ 2 / 1
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◎，规则如下：\n实数域上，x ◎ y = (x * y + 1) + 3 - x。\n和 □，规则如下：\n当x是奇数时，x □ y = x + y ◎ y；\n其他情况下，x □ y = x - y ** y - x + x。\n运算优先级：□ > ◎ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 ◎ 8 □ 2 / 1\n请将最终答案填入\\boxed{}中。"
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logic-v2 | Define □, the rules are as follows:
when x is greater than y, x □ y = x * y * y - 3;
otherwise, x □ y = x - y - x - y.
and ○, the rules are as follows:
when y is a multiple of 5, x ○ y = y * y - x ** y;
otherwise, x ○ y = y + x + x * y.
The precedence of operations: ○ > ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ○ 8 □ 2
Please fill your final answer in \boxed{}. | {
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"question": "Define □, the rules are as follows:\nwhen x is greater than y, x □ y = x * y * y - 3;\notherwise, x □ y = x - y - x - y.\nand ○, the rules are as follows:\nwhen y is a multiple of 5, x ○ y = y * y - x ** y;\notherwise, x ○ y = y + x + x * y.\nThe precedence of operations: ○ > ** = □ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ○ 8 □ 2\nPlease fill your final answer in \\boxed{}."
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logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = y / x + y * y。
运算优先级：** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ◇ 9
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x * abs(x + x * x) + y。
运算优先级：** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ◇ 8 / 2 % 6
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = 4 * y / y - x.
and ♢, the rules are as follows:
when the sum of x and y is odd, x ♢ y = (y) * x;
otherwise, x ♢ y = x * x ◎ y - x.
The precedence of operations: ◎ > ** = ♢ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ♢ 7 % 9 ◎ 1 / 5
Please fill your final answer in \boxed{}. | {
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = 4 * y / y - x.\nand ♢, the rules are as follows:\nwhen the sum of x and y is odd, x ♢ y = (y) * x;\notherwise, x ♢ y = x * x ◎ y - x.\nThe precedence of operations: ◎ > ** = ♢ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ♢ 7 % 9 ◎ 1 / 5\nPlease fill your final answer in \\boxed{}."
},
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"seed": 98179543,
"simplified_expr": "((((((((7 * (( 4 * 7 / 7 - 7)))) - 7))) % (( 4 * 1 / 1 - 9)))) / 5)",
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"operation": " (y) * x"
}
],
"default_operation": " x * x ◎ y - x",
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}
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"seed": 98179543,
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} |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y + y * y - y * x.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6
Please fill your final answer in \boxed{}. | {
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"answer": "6",
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"question": "Define ◇, the rules are as follows:\non the real number field, x ◇ y = y + y * y - y * x.\nThe precedence of operations: ◇ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "6",
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"△": null,
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"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " y + y * y - y * x",
"precedence": 4
},
"○": null,
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"☆": null,
"♡": null,
"♢": null
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x * y / y。
和 ♢，规则如下：
当x等于y时，x ♢ y = (x) ⊗ y；
其他情况下，x ♢ y = y ⊗ x / y。
和 ◎，规则如下：
实数域上，x ◎ y = y * x ⊗ x。
运算优先级：♢ > ** > * = / = % > + = - = ⊗ = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊗ 5 ♢ 1
请将最终答案填入\boxed{}中。 | {
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"condition": "x等于y",
"operation": " (x) ⊗ y"
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"default_operation": " y ⊗ x / y",
"precedence": 5
}
},
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"trace_id": "f016bfe7-ea48-4488-b04b-d55c126cf221"
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = x * y / y。\n和 ♢，规则如下：\n当x等于y时，x ♢ y = (x) ⊗ y；\n其他情况下，x ♢ y = y ⊗ x / y。\n和 ◎，规则如下：\n实数域上，x ◎ y = y * x ⊗ x。\n运算优先级：♢ > ** > * = / = % > + = - = ⊗ = ◎。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2 ⊗ 5 ♢ 1\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "2 ⊗ 5 ♢ 1",
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"seed": 9947946,
"simplified_expr": "( 2 * ((( 1 * ((5 / 1)) / ((5 / 1))))) / ((( 1 * ((5 / 1)) / ((5 / 1))))))",
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"△": null,
"▽": null,
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"○": null,
"◎": {
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"default_operation": " y * x ⊗ x",
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},
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " (x) ⊗ y"
}
],
"default_operation": " y ⊗ x / y",
"precedence": 5
}
},
"target": null,
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"trace_id": "f016bfe7-ea48-4488-b04b-d55c126cf221"
},
"seed": 9947946,
"task_id": 209947946,
"task_type": "operation"
} |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = 5 * y + 5 + x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 △ 9 ** 3 / 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 △，规则如下：\n实数域上，x △ y = 5 * y + 5 + x。\n运算优先级：** > * = / = % = △ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2 △ 9 ** 3 / 4\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"seed": 12382364,
"simplified_expr": "((( 5 * ((9 ** 3)) + 5 + 2)) / 4)",
"solutions_count": null,
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"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " 5 * y + 5 + x",
"precedence": 2
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
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"seed": 12382364,
"task_id": 212382364,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = x + y + 2 + x - 2;
otherwise, x ▽ y = 3 + x * y - x.
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 - 9 ▽ 3
Please fill your final answer in \boxed{}. | {
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"◇": null,
"○": null,
"◎": null,
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"♢": null
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"question": "Define ▽, the rules are as follows:\nwhen the sum of x and y is even, x ▽ y = x + y + 2 + x - 2;\notherwise, x ▽ y = 3 + x * y - x.\nThe precedence of operations: ** > * = / = % > + = - = ▽。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 - 9 ▽ 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"solutions_count": null,
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"△": null,
"▽": {
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"conditions": [
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"operation": " x + y + 2 + x - 2"
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],
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"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"seed": 96695313,
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"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x - abs(x * y).
and ▽, the rules are as follows:
when x is equal to y, x ▽ y = x + x - y;
otherwise, x ▽ y = y + (x - y).
and △, the rules are as follows:
when x is less than y, x △ y = x / abs(x - y);
otherwise, x △ y = y + (x + 2).
The precedence of operations: ◎ = △ > ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ▽ 9 △ 5 ◎ 5
Please fill your final answer in \boxed{}. | {
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"conditions": [
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"operation": " x + x - y"
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"default_operation": " y + (x - y)",
"precedence": 2
},
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
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"precedence": 5
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "9cb00eca-f9f7-4a84-8fa2-9de2c3f42367"
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = x - abs(x * y).\nand ▽, the rules are as follows:\nwhen x is equal to y, x ▽ y = x + x - y;\notherwise, x ▽ y = y + (x - y).\nand △, the rules are as follows:\nwhen x is less than y, x △ y = x / abs(x - y);\notherwise, x △ y = y + (x + 2).\nThe precedence of operations: ◎ = △ > ** > * = / = % = ▽ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 ▽ 9 △ 5 ◎ 5\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( (( (( 5 + (9 + 2))) - abs((( 5 + (9 + 2))) * 5))) + (6 - (( (( 5 + (9 + 2))) - abs((( 5 + (9 + 2))) * 5)))))",
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"condition": "x小于y",
"operation": " x / abs(x - y)"
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],
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"precedence": 5
},
"▽": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " x + x - y"
}
],
"default_operation": " y + (x - y)",
"precedence": 2
},
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
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"precedence": 5
},
"☆": null,
"♡": null,
"♢": null
},
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y + x - x。
和 ⊙，规则如下：
实数域上，x ⊙ y = x ⊗ y * y。
和 ◇，规则如下：
当y是偶数时，x ◇ y = y * y ⊗ x；
其他情况下，x ◇ y = x + y。
运算优先级：◇ > ** > * = / = % = ⊗ = ⊙ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◇ 10 ⊗ 2 / 1 ⊙ 7
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = y + x - x。\n和 ⊙，规则如下：\n实数域上，x ⊙ y = x ⊗ y * y。\n和 ◇，规则如下：\n当y是偶数时，x ◇ y = y * y ⊗ x；\n其他情况下，x ◇ y = x + y。\n运算优先级：◇ > ** > * = / = % = ⊗ = ⊙ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 ◇ 10 ⊗ 2 / 1 ⊙ 7\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x * y - x.
and □, the rules are as follows:
on the real number field, x □ y = x ♢ y ** y.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = y + x * y;
otherwise, x ♡ y = x ♢ y * 2.
The precedence of operations: □ > ** = ♡ > * = / = % > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 □ 5 ♡ 8 ♡ 7 ♢ 1
Please fill your final answer in \boxed{}. | {
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"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = x * y - x.\nand □, the rules are as follows:\non the real number field, x □ y = x ♢ y ** y.\nand ♡, the rules are as follows:\nwhen the sum of x and y is odd, x ♡ y = y + x * y;\notherwise, x ♡ y = x ♢ y * 2.\nThe precedence of operations: □ > ** = ♡ > * = / = % > + = - = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 □ 5 ♡ 8 ♡ 7 ♢ 1\nPlease fill your final answer in \\boxed{}."
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"operation": " y + x * y"
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x * y + x。
和 △，规则如下：
实数域上，x △ y = x ⊕ x + y。
和 ♡，规则如下：
实数域上，x ♡ y = x + y。
运算优先级：△ > ** = ♡ > * = / = % = ⊕ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 △ 3 ♡ 7 ⊕ 7
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊕，规则如下：\n实数域上，x ⊕ y = x * y + x。\n和 △，规则如下：\n实数域上，x △ y = x ⊕ x + y。\n和 ♡，规则如下：\n实数域上，x ♡ y = x + y。\n运算优先级：△ > ** = ♡ > * = / = % = ⊕ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 △ 3 ♡ 7 ⊕ 7\n请将最终答案填入\\boxed{}中。"
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logic-v2 | Define ▽, the rules are as follows:
when x is equal to y, x ▽ y = y * x + 2;
otherwise, x ▽ y = x / y - y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ▽ 1 ▽ 9
Please fill your final answer in \boxed{}. | {
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},
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} |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x - y * x - y.
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 3 △ 7
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x - 5 * abs(y).
and ⊕, the rules are as follows:
when x and y are both odd, x ⊕ y = y + x * x;
otherwise, x ⊕ y = y - y + x + x.
The precedence of operations: □ > ** > * = / = % > + = - = ⊕。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ⊕ 2
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | 定义 ◎，规则如下：
当x是3的倍数时，x ◎ y = y * x；
其他情况下，x ◎ y = y + 4 * y * x。
和 △，规则如下：
实数域上，x △ y = abs(x + x) * y + y。
运算优先级：◎ = △ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 △ 8 ◎ 6 * 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◎，规则如下：\n当x是3的倍数时，x ◎ y = y * x；\n其他情况下，x ◎ y = y + 4 * y * x。\n和 △，规则如下：\n实数域上，x △ y = abs(x + x) * y + y。\n运算优先级：◎ = △ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 7 △ 8 ◎ 6 * 10\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = (y - y - y) * x.
and ♢, the rules are as follows:
when x is a multiple of 5, x ♢ y = x * y + x ⊗ y;
otherwise, x ♢ y = (x) * x * y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y - x * y.
The precedence of operations: ⊕ > ** > * = / = % > + = - = ⊗ = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ⊗ 6 ♢ 6 ⊕ 1
Please fill your final answer in \boxed{}. | {
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"condition": "x是5的倍数",
"operation": " x * y + x ⊗ y"
}
],
"default_operation": " (x) * x * y",
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}
},
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"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = (y - y - y) * x.\nand ♢, the rules are as follows:\nwhen x is a multiple of 5, x ♢ y = x * y + x ⊗ y;\notherwise, x ♢ y = (x) * x * y.\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = y - x * y.\nThe precedence of operations: ⊕ > ** > * = / = % > + = - = ⊗ = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ⊗ 6 ♢ 6 ⊕ 1\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( ((( (6 - 6 - 6) * 7))) * (( (6 - 6 - 6) * 7)) * (( 1 - 6 * 1)))",
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"operation": " x * y + x ⊗ y"
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],
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logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + 2 * y.
and ○, the rules are as follows:
on the real number field, x ○ y = 5 / y ⊕ x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x ⊕ y * y.
The precedence of operations: ⊕ > ⊗ > ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ○ 3 ⊗ 1 ⊕ 4
Please fill your final answer in \boxed{}. | {
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"◎": null,
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"♢": null
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"target": null,
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"trace_id": "d0bfad38-6bb9-4513-81ac-f63ca9ac4094"
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"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = x + 2 * y.\nand ○, the rules are as follows:\non the real number field, x ○ y = 5 / y ⊕ x.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = x ⊕ y * y.\nThe precedence of operations: ⊕ > ⊗ > ** = ○ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ○ 3 ⊗ 1 ⊕ 4\nPlease fill your final answer in \\boxed{}."
},
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"seed": 16545748,
"simplified_expr": "((5 / (( ((((3 + ((2 * ((1 + ((2 * 4)))))))) * ((1 + ((2 * 4)))))) + 2 * 4))))",
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"default_operation": " 5 / y ⊕ x",
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},
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"♢": null
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logic-v2 | Define ⊕, the rules are as follows:
when x is a multiple of 5, x ⊕ y = x * x / y;
otherwise, x ⊕ y = y ** x - y.
and ♡, the rules are as follows:
when y is odd, x ♡ y = x * 1 + y;
otherwise, x ♡ y = y ⊕ x * y.
and ○, the rules are as follows:
on the real number field, x ○ y = y + x * y.
The precedence of operations: ○ > ** = ⊕ = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ○ 8 ♡ 3
Please fill your final answer in \boxed{}. | {
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"△": null,
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"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
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"condition": "y是奇数",
"operation": " x * 1 + y"
}
],
"default_operation": " y ⊕ x * y",
"precedence": 3
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "e3f4dea7-6aa9-49fb-bdf5-cc1f65e2758e"
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"question": "Define ⊕, the rules are as follows:\nwhen x is a multiple of 5, x ⊕ y = x * x / y;\notherwise, x ⊕ y = y ** x - y.\nand ♡, the rules are as follows:\nwhen y is odd, x ♡ y = x * 1 + y;\notherwise, x ♡ y = y ⊕ x * y.\nand ○, the rules are as follows:\non the real number field, x ○ y = y + x * y.\nThe precedence of operations: ○ > ** = ⊕ = ♡ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ○ 8 ♡ 3\nPlease fill your final answer in \\boxed{}."
},
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"□": null,
"△": null,
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},
"◎": null,
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"♡": {
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"conditions": [
{
"condition": "y是奇数",
"operation": " x * 1 + y"
}
],
"default_operation": " y ⊕ x * y",
"precedence": 3
},
"♢": null
},
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logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x + y ** (y)。
和 ♡，规则如下：
实数域上，x ♡ y = y + x。
运算优先级：□ = ♡ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 6
请将最终答案填入\boxed{}中。 | {
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"question": "定义 □，规则如下：\n实数域上，x □ y = x + y ** (y)。\n和 ♡，规则如下：\n实数域上，x ♡ y = y + x。\n运算优先级：□ = ♡ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 ♡ 6\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y * x。
和 ⊗，规则如下：
当x是奇数时，x ⊗ y = x + y；
其他情况下，x ⊗ y = (y - 3 * x)。
运算优先级：□ > ** > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 □ 4 ⊗ 5
请将最终答案填入\boxed{}中。 | {
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"question": "定义 □，规则如下：\n实数域上，x □ y = y * x。\n和 ⊗，规则如下：\n当x是奇数时，x ⊗ y = x + y；\n其他情况下，x ⊗ y = (y - 3 * x)。\n运算优先级：□ > ** > * = / = % > + = - = ⊗。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 □ 4 ⊗ 5\n请将最终答案填入\\boxed{}中。"
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logic-v2 | 定义 △，规则如下：
当x和y都是奇数时，x △ y = y * x - x；
其他情况下，x △ y = x / y * y。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 △ 2 / 3
请将最终答案填入\boxed{}中。 | {
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"condition": "x和y都是奇数",
"operation": " y * x - x"
}
],
"default_operation": " x / y * y",
"precedence": 5
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
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"♡": null,
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"question": "定义 △，规则如下：\n当x和y都是奇数时，x △ y = y * x - x；\n其他情况下，x △ y = x / y * y。\n运算优先级：△ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 △ 2 / 3\n请将最终答案填入\\boxed{}中。"
},
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"expression": "4 △ 2 / 3",
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"seed": 55785221,
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} |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = 1 - y - x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 1 - (y + x) + 5.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y ** x + y - y.
The precedence of operations: ⊗ = ◇ = ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ◇ 3 ▽ 7 ⊗ 7 ◇ 4
Please fill your final answer in \boxed{}. | {
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"conditions": [],
"default_operation": " y ** x + y - y",
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"conditions": [],
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"precedence": 4
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"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = 1 - y - x.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = 1 - (y + x) + 5.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = y ** x + y - y.\nThe precedence of operations: ⊗ = ◇ = ▽ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ◇ 3 ▽ 7 ⊗ 7 ◇ 4\nPlease fill your final answer in \\boxed{}."
},
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"seed": 83930224,
"simplified_expr": "( 1 - (4 + (( 1 - 7 - (( 7 ** (( 1 - (3 + 2) + 5)) + 7 - 7))))) + 5)",
"solutions_count": null,
"symbol_definitions": {
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"⊗": {
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"default_operation": " 1 - y - x",
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"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " y ** x + y - y",
"precedence": 4
},
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " 1 - (y + x) + 5",
"precedence": 4
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "f45fa079-65ee-4dcc-afd4-48ba10a9aefd"
},
"seed": 83930224,
"task_id": 283930224,
"task_type": "operation"
} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x * y - y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y / x / x.
The precedence of operations: ☆ > ** > * = / = % > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ⊗ 10 ⊗ 4 ☆ 5
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "( (( 4 * 5 - 5)) / (( 10 / 9 / 9)) / (( 10 / 9 / 9)))",
"solutions_count": null,
"symbol_definitions": {
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
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"associativity": "left",
"conditions": [],
"default_operation": " x * y - y",
"precedence": 4
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"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "bea902a5-1647-42d3-8e0b-95593b822233"
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = x * y - y.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = y / x / x.\nThe precedence of operations: ☆ > ** > * = / = % > + = - = ⊗。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 ⊗ 10 ⊗ 4 ☆ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 10 ⊗ 4 ☆ 5",
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"seed": 28182757,
"simplified_expr": "( (( 4 * 5 - 5)) / (( 10 / 9 / 9)) / (( 10 / 9 / 9)))",
"solutions_count": null,
"symbol_definitions": {
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y - y",
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},
"♡": null,
"♢": null
},
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"trace_id": "bea902a5-1647-42d3-8e0b-95593b822233"
},
"seed": 28182757,
"task_id": 228182757,
"task_type": "operation"
} |
logic-v2 | 定义 ⊙，规则如下：
当x等于y时，x ⊙ y = 2 + (y / 4) + x；
其他情况下，x ⊙ y = y / y + 4 + x。
和 ☆，规则如下：
当y是3的倍数时，x ☆ y = x ** y；
其他情况下，x ☆ y = x ⊙ y * y + y。
和 ◎，规则如下：
实数域上，x ◎ y = x - x + x + y。
运算优先级：☆ > ** = ◎ > * = / = % = ⊙ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◎ 2 ⊙ 3 ☆ 7
请将最终答案填入\boxed{}中。 | {
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
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"default_operation": " x - x + x + y",
"precedence": 3
},
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "y是3的倍数",
"operation": " x ** y"
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],
"default_operation": " x ⊙ y * y + y",
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"♡": null,
"♢": null
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"target": null,
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"question": "定义 ⊙，规则如下：\n当x等于y时，x ⊙ y = 2 + (y / 4) + x；\n其他情况下，x ⊙ y = y / y + 4 + x。\n和 ☆，规则如下：\n当y是3的倍数时，x ☆ y = x ** y；\n其他情况下，x ☆ y = x ⊙ y * y + y。\n和 ◎，规则如下：\n实数域上，x ◎ y = x - x + x + y。\n运算优先级：☆ > ** = ◎ > * = / = % = ⊙ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 ◎ 2 ⊙ 3 ☆ 7\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "8 ◎ 2 ⊙ 3 ☆ 7",
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"simplified_expr": "( ((((((( 7 / 7 + 4 + 3)) * 7)) + 7))) / ((((((( 7 / 7 + 4 + 3)) * 7)) + 7))) + 4 + (( 8 - 8 + 8 + 2)))",
"solutions_count": null,
"symbol_definitions": {
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"operation": " 2 + (y / 4) + x"
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],
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
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"default_operation": " x - x + x + y",
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},
"☆": {
"associativity": "left",
"conditions": [
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"condition": "y是3的倍数",
"operation": " x ** y"
}
],
"default_operation": " x ⊙ y * y + y",
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"♡": null,
"♢": null
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"target": null,
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},
"seed": 22802174,
"task_id": 222802174,
"task_type": "operation"
} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y + x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y / x * y.
and ◇, the rules are as follows:
when y is even, x ◇ y = y - x * (x);
otherwise, x ◇ y = (x) * x - y.
The precedence of operations: ** = ♢ = ♡ > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ◇ 6 ◇ 5 ♡ 2 ♢ 7 + 1
Please fill your final answer in \boxed{}. | {
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"precedence": 2
},
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x * y",
"precedence": 3
},
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x",
"precedence": 3
}
},
"target": null,
"total_length": null,
"trace_id": "d264602a-79d1-416a-b873-febee698c1ec"
},
"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = y + x.\nand ♡, the rules are as follows:\non the real number field, x ♡ y = y / x * y.\nand ◇, the rules are as follows:\nwhen y is even, x ◇ y = y - x * (x);\notherwise, x ◇ y = (x) * x - y.\nThe precedence of operations: ** = ♢ = ♡ > * = / = % = ◇ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 ◇ 6 ◇ 5 ♡ 2 ♢ 7 + 1\nPlease fill your final answer in \\boxed{}."
},
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"expression": "9 ◇ 6 ◇ 5 ♡ 2 ♢ 7 + 1",
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"△": null,
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"◎": null,
"☆": null,
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"conditions": [],
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},
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"associativity": "left",
"conditions": [],
"default_operation": " y + x",
"precedence": 3
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"seed": 58463316,
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} |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * y - x ** y。
和 ⊙，规则如下：
当x是5的倍数时，x ⊙ y = 3 + x - y + x；
其他情况下，x ⊙ y = y / x - y + 4。
运算优先级：** = ⊙ > * = / = % > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 4 ⊙ 6
请将最终答案填入\boxed{}中。 | {
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"△": null,
"▽": null,
"◇": null,
"○": null,
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"☆": null,
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"♢": null
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"target": null,
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"question": "定义 □，规则如下：\n实数域上，x □ y = x * y - x ** y。\n和 ⊙，规则如下：\n当x是5的倍数时，x ⊙ y = 3 + x - y + x；\n其他情况下，x ⊙ y = y / x - y + 4。\n运算优先级：** = ⊙ > * = / = % > + = - = □。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 □ 4 ⊙ 6\n请将最终答案填入\\boxed{}中。"
},
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"expression": "1 □ 4 ⊙ 6",
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"num_symbols": 2,
"numbers": null,
"operators": null,
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"seed": 78109538,
"simplified_expr": "( 1 * (( 6 / 4 - 6 + 4)) - 1 ** (( 6 / 4 - 6 + 4)))",
"solutions_count": null,
"symbol_definitions": {
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"operation": " 3 + x - y + x"
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],
"default_operation": " y / x - y + 4",
"precedence": 3
},
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y - x ** y",
"precedence": 1
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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},
"seed": 78109538,
"task_id": 278109538,
"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x - x * y.
and □, the rules are as follows:
when x is even, x □ y = x ◎ y;
otherwise, x □ y = y - x + x.
The precedence of operations: ◎ > ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 □ 1
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = 3 - y * x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y + x + x.
The precedence of operations: ⊗ > ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ⊗ 5 ♡ 3 ⊗ 7
Please fill your final answer in \boxed{}. | {
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"question": "Define ♡, the rules are as follows:\non the real number field, x ♡ y = 3 - y * x.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = y + x + x.\nThe precedence of operations: ⊗ > ♡ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 ⊗ 5 ♡ 3 ⊗ 7\nPlease fill your final answer in \\boxed{}."
},
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"□": null,
"△": null,
"▽": null,
"◇": null,
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"◎": null,
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"♡": {
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} |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = y + x。
和 ▽，规则如下：
实数域上，x ▽ y = x - x ♢ x ** y。
和 ○，规则如下：
实数域上，x ○ y = x + 3 * x - y。
运算优先级：♢ = ○ > ** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ○ 10 ♢ 7
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ♢，规则如下：\n实数域上，x ♢ y = y + x。\n和 ▽，规则如下：\n实数域上，x ▽ y = x - x ♢ x ** y。\n和 ○，规则如下：\n实数域上，x ○ y = x + 3 * x - y。\n运算优先级：♢ = ○ > ** > * = / = % = ▽ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2 ○ 10 ♢ 7\n请将最终答案填入\\boxed{}中。"
},
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"task_type": "operation"
} |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y + x + y。
和 ⊕，规则如下：
当y是5的倍数时，x ⊕ y = y * y / x；
其他情况下，x ⊕ y = x - y ⊗ x。
和 ☆，规则如下：
实数域上，x ☆ y = y ⊗ 2 + x。
运算优先级：⊗ > ** > * = / = % = ⊕ > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 * 2 ☆ 2 ⊗ 1 + 10 ⊕ 9
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = y + x + y。\n和 ⊕，规则如下：\n当y是5的倍数时，x ⊕ y = y * y / x；\n其他情况下，x ⊕ y = x - y ⊗ x。\n和 ☆，规则如下：\n实数域上，x ☆ y = y ⊗ 2 + x。\n运算优先级：⊗ > ** > * = / = % = ⊕ > + = - = ☆。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 * 2 ☆ 2 ⊗ 1 + 10 ⊕ 9\n请将最终答案填入\\boxed{}中。"
},
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},
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"♢": null
},
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logic-v2 | Define ▽, the rules are as follows:
when y is a multiple of 5, x ▽ y = y - abs(x / x);
otherwise, x ▽ y = x + y.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ▽ 6 ▽ 9
Please fill your final answer in \boxed{}. | {
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},
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"△": null,
"▽": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " y - abs(x / x)"
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],
"default_operation": " x + y",
"precedence": 2
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"seed": 71077131,
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} |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y / x * x.
and ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = y △ x + y;
otherwise, x ⊙ y = x - y * x.
The precedence of operations: △ > ** > * = / = % > + = - = ⊙。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 △ 9
Please fill your final answer in \boxed{}. | {
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"default_operation": " x - y * x",
"precedence": 1
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"□": null,
"△": {
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},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "75bcb8ce-5b39-4185-b06a-57285d5dac37"
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"question": "Define △, the rules are as follows:\non the real number field, x △ y = y / x * x.\nand ⊙, the rules are as follows:\nwhen x and y are both odd, x ⊙ y = y △ x + y;\notherwise, x ⊙ y = x - y * x.\nThe precedence of operations: △ > ** > * = / = % > + = - = ⊙。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 △ 9\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "6 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
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"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 59019643,
"simplified_expr": "( 9 / 6 * 6)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [
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"condition": "x和y都是奇数",
"operation": " y △ x + y"
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],
"default_operation": " x - y * x",
"precedence": 1
},
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x * x",
"precedence": 4
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"target": null,
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"trace_id": "75bcb8ce-5b39-4185-b06a-57285d5dac37"
},
"seed": 59019643,
"task_id": 259019643,
"task_type": "operation"
} |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * y * (y - x).
and ◇, the rules are as follows:
when x is less than y, x ◇ y = y * x - y - y;
otherwise, x ◇ y = x ⊙ 3 - y + (x).
and ◎, the rules are as follows:
on the real number field, x ◎ y = y / x ** x + x.
The precedence of operations: ◎ > ** = ⊙ = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ◇ 1 ◎ 3
Please fill your final answer in \boxed{}. | {
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"operators": null,
"question_sequence": null,
"seed": 14650444,
"simplified_expr": "(((((( 3 * 3 * (3 - 8))) - ((((3 / ((1 ** 1)))) + 1)))) + 8))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y * (y - x)",
"precedence": 3
},
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " y * x - y - y"
}
],
"default_operation": " x ⊙ 3 - y + (x)",
"precedence": 3
},
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x ** x + x",
"precedence": 4
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "132dcaaa-91af-4876-8a6c-0fa26650d622"
},
"question": "Define ⊙, the rules are as follows:\non the real number field, x ⊙ y = y * y * (y - x).\nand ◇, the rules are as follows:\nwhen x is less than y, x ◇ y = y * x - y - y;\notherwise, x ◇ y = x ⊙ 3 - y + (x).\nand ◎, the rules are as follows:\non the real number field, x ◎ y = y / x ** x + x.\nThe precedence of operations: ◎ > ** = ⊙ = ◇ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 8 ◇ 1 ◎ 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 1 ◎ 3",
"fill_length": null,
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"is_solvable": null,
"language": "english",
"n_types": null,
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"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 14650444,
"simplified_expr": "(((((( 3 * 3 * (3 - 8))) - ((((3 / ((1 ** 1)))) + 1)))) + 8))",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
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"conditions": [],
"default_operation": " y * y * (y - x)",
"precedence": 3
},
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " y * x - y - y"
}
],
"default_operation": " x ⊙ 3 - y + (x)",
"precedence": 3
},
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x ** x + x",
"precedence": 4
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "132dcaaa-91af-4876-8a6c-0fa26650d622"
},
"seed": 14650444,
"task_id": 214650444,
"task_type": "operation"
} |
logic-v2 | Define ♢, the rules are as follows:
when x is a multiple of 3, x ♢ y = x ** 4 / x ** x + y;
otherwise, x ♢ y = 3 + y - x - 2 - x.
and ◎, the rules are as follows:
when y is even, x ◎ y = y + x ** y;
otherwise, x ◎ y = y * x * x - x + x.
and ☆, the rules are as follows:
when x is a multiple of 3, x ☆ y = y - x / x - y / 3;
otherwise, x ☆ y = x + (y + y + x + x).
The precedence of operations: ◎ = ☆ > ** > * = / = % > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ☆ 4 ☆ 3 ♢ 1 ◎ 5
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 4 ☆ 3 ♢ 1 ◎ 5",
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"n_types": null,
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"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
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"seed": 65017318,
"simplified_expr": "( (( (( 10 + (4 + 4 + 10 + 10))) + (3 + 3 + (( 10 + (4 + 4 + 10 + 10))) + (( 10 + (4 + 4 + 10 + 10)))))) ** 4 / (( (( 10 + (4 + 4 + 10 + 10))) + (3 + 3 + (( 10 + (4 + 4 + 10 + 10))) + (( 10 + (4 + 4 + 10 + 10)))))) ** (( (( 10 + (4 + 4 + 10 + 10))) + (3 + 3 + (( 10 + (4 + 4 + 10 + 10))) + (( 10 + (4 + 4 + 10 + 10)))))) + (( 5 * 1 * 1 - 1 + 1)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "y是偶数",
"operation": " y + x ** y"
}
],
"default_operation": " y * x * x - x + x",
"precedence": 4
},
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " y - x / x - y / 3"
}
],
"default_operation": " x + (y + y + x + x)",
"precedence": 4
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " x ** 4 / x ** x + y"
}
],
"default_operation": " 3 + y - x - 2 - x",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "351dad74-2533-48dd-9c89-f6ec67252148"
},
"question": "Define ♢, the rules are as follows:\nwhen x is a multiple of 3, x ♢ y = x ** 4 / x ** x + y;\notherwise, x ♢ y = 3 + y - x - 2 - x.\nand ◎, the rules are as follows:\nwhen y is even, x ◎ y = y + x ** y;\notherwise, x ◎ y = y * x * x - x + x.\nand ☆, the rules are as follows:\nwhen x is a multiple of 3, x ☆ y = y - x / x - y / 3;\notherwise, x ☆ y = x + (y + y + x + x).\nThe precedence of operations: ◎ = ☆ > ** > * = / = % > + = - = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 ☆ 4 ☆ 3 ♢ 1 ◎ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 4 ☆ 3 ♢ 1 ◎ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
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"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 65017318,
"simplified_expr": "( (( (( 10 + (4 + 4 + 10 + 10))) + (3 + 3 + (( 10 + (4 + 4 + 10 + 10))) + (( 10 + (4 + 4 + 10 + 10)))))) ** 4 / (( (( 10 + (4 + 4 + 10 + 10))) + (3 + 3 + (( 10 + (4 + 4 + 10 + 10))) + (( 10 + (4 + 4 + 10 + 10)))))) ** (( (( 10 + (4 + 4 + 10 + 10))) + (3 + 3 + (( 10 + (4 + 4 + 10 + 10))) + (( 10 + (4 + 4 + 10 + 10)))))) + (( 5 * 1 * 1 - 1 + 1)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "y是偶数",
"operation": " y + x ** y"
}
],
"default_operation": " y * x * x - x + x",
"precedence": 4
},
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " y - x / x - y / 3"
}
],
"default_operation": " x + (y + y + x + x)",
"precedence": 4
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " x ** 4 / x ** x + y"
}
],
"default_operation": " 3 + y - x - 2 - x",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "351dad74-2533-48dd-9c89-f6ec67252148"
},
"seed": 65017318,
"task_id": 265017318,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = y * y + x / x * y;
otherwise, x ▽ y = 5 - x + x + y + y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ▽ 5
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 17109992,
"simplified_expr": "( 5 - 7 + 7 + 5 + 5)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
{
"condition": "y是3的倍数",
"operation": " y * y + x / x * y"
}
],
"default_operation": " 5 - x + x + y + y",
"precedence": 5
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "1e1ac4c9-4eb2-4292-828b-c9d1c031dc52"
},
"question": "Define ▽, the rules are as follows:\nwhen y is a multiple of 3, x ▽ y = y * y + x / x * y;\notherwise, x ▽ y = 5 - x + x + y + y.\nThe precedence of operations: ▽ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ▽ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 17109992,
"simplified_expr": "( 5 - 7 + 7 + 5 + 5)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
{
"condition": "y是3的倍数",
"operation": " y * y + x / x * y"
}
],
"default_operation": " 5 - x + x + y + y",
"precedence": 5
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "1e1ac4c9-4eb2-4292-828b-c9d1c031dc52"
},
"seed": 17109992,
"task_id": 217109992,
"task_type": "operation"
} |
logic-v2 | Define △, the rules are as follows:
when y is odd, x △ y = y / (1 * x);
otherwise, x △ y = y + abs(x).
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 △ 8
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 40387779,
"simplified_expr": "( 8 + abs(5))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y / (1 * x)"
}
],
"default_operation": " y + abs(x)",
"precedence": 5
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "db34b282-5948-4bf3-bfd0-907710c6a656"
},
"question": "Define △, the rules are as follows:\nwhen y is odd, x △ y = y / (1 * x);\notherwise, x △ y = y + abs(x).\nThe precedence of operations: △ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 △ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "5 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 40387779,
"simplified_expr": "( 8 + abs(5))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y / (1 * x)"
}
],
"default_operation": " y + abs(x)",
"precedence": 5
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "db34b282-5948-4bf3-bfd0-907710c6a656"
},
"seed": 40387779,
"task_id": 240387779,
"task_type": "operation"
} |
logic-v2 | Define △, the rules are as follows:
when x is greater than y, x △ y = abs(y - x - y) - 2;
otherwise, x △ y = y + x + x / x.
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 △ 4 △ 8
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 4 △ 8",
"fill_length": null,
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"n_types": null,
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"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 2831582,
"simplified_expr": "( 8 + (( 4 + 3 + 3 / 3)) + (( 4 + 3 + 3 / 3)) / (( 4 + 3 + 3 / 3)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " abs(y - x - y) - 2"
}
],
"default_operation": " y + x + x / x",
"precedence": 1
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "bb9c0178-7533-4e4d-89b1-90e33fd90a87"
},
"question": "Define △, the rules are as follows:\nwhen x is greater than y, x △ y = abs(y - x - y) - 2;\notherwise, x △ y = y + x + x / x.\nThe precedence of operations: ** > * = / = % > + = - = △。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 △ 4 △ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "3 △ 4 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 2831582,
"simplified_expr": "( 8 + (( 4 + 3 + 3 / 3)) + (( 4 + 3 + 3 / 3)) / (( 4 + 3 + 3 / 3)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " abs(y - x - y) - 2"
}
],
"default_operation": " y + x + x / x",
"precedence": 1
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "bb9c0178-7533-4e4d-89b1-90e33fd90a87"
},
"seed": 2831582,
"task_id": 202831582,
"task_type": "operation"
} |
logic-v2 | Define ⊗, the rules are as follows:
when x is odd, x ⊗ y = y - x * x;
otherwise, x ⊗ y = y - x - x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (y) - x - x.
and □, the rules are as follows:
when y is odd, x □ y = y - y / x;
otherwise, x □ y = 3 ☆ y + x.
The precedence of operations: ** = □ > * = / = % > + = - = ⊗ = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ⊗ 2 □ 6 / 6 ☆ 5
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "32.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 2 □ 6 / 6 ☆ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
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"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 89444342,
"simplified_expr": "( (5) - (( ((((((( (6) - 3 - 3)) + 2))) / 6)) - 7 - 7)) - (( ((((((( (6) - 3 - 3)) + 2))) / 6)) - 7 - 7)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
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"conditions": [
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"condition": "x是奇数",
"operation": " y - x * x"
}
],
"default_operation": " y - x - x",
"precedence": 1
},
"⊙": null,
"□": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y - y / x"
}
],
"default_operation": " 3 ☆ y + x",
"precedence": 3
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " (y) - x - x",
"precedence": 1
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "7c2bef42-f3d1-422f-842d-a57ee97cd361"
},
"question": "Define ⊗, the rules are as follows:\nwhen x is odd, x ⊗ y = y - x * x;\notherwise, x ⊗ y = y - x - x.\nand ☆, the rules are as follows:\non the real number field, x ☆ y = (y) - x - x.\nand □, the rules are as follows:\nwhen y is odd, x □ y = y - y / x;\notherwise, x □ y = 3 ☆ y + x.\nThe precedence of operations: ** = □ > * = / = % > + = - = ⊗ = ☆。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ⊗ 2 □ 6 / 6 ☆ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 2 □ 6 / 6 ☆ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 89444342,
"simplified_expr": "( (5) - (( ((((((( (6) - 3 - 3)) + 2))) / 6)) - 7 - 7)) - (( ((((((( (6) - 3 - 3)) + 2))) / 6)) - 7 - 7)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [
{
"condition": "x是奇数",
"operation": " y - x * x"
}
],
"default_operation": " y - x - x",
"precedence": 1
},
"⊙": null,
"□": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y - y / x"
}
],
"default_operation": " 3 ☆ y + x",
"precedence": 3
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " (y) - x - x",
"precedence": 1
},
"♡": null,
"♢": null
},
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logic-v2 | Define ◇, the rules are as follows:
when x is a multiple of 3, x ◇ y = y + y - 1 + x;
otherwise, x ◇ y = x + x + 4 ** y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ** 10 ◇ 5 ** 9
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x + (4) / y.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ◇ 1
Please fill your final answer in \boxed{}. | {
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},
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"○": null,
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logic-v2 | Define ☆, the rules are as follows:
when x is greater than y, x ☆ y = x - x - y;
otherwise, x ☆ y = x - (3 - y).
and ◎, the rules are as follows:
on the real number field, x ◎ y = y ☆ x * y.
The precedence of operations: ** = ◎ > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ◎ 10 ☆ 9
Please fill your final answer in \boxed{}. | {
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"☆": {
"associativity": "left",
"conditions": [
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"operation": " x - x - y"
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],
"default_operation": " x - (3 - y)",
"precedence": 1
},
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "5338fc3d-37e8-4173-8a6f-ad82be266de2"
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"question": "Define ☆, the rules are as follows:\nwhen x is greater than y, x ☆ y = x - x - y;\notherwise, x ☆ y = x - (3 - y).\nand ◎, the rules are as follows:\non the real number field, x ◎ y = y ☆ x * y.\nThe precedence of operations: ** = ◎ > * = / = % > + = - = ☆。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 ◎ 10 ☆ 9\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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],
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} |
logic-v2 | 定义 ◎，规则如下：
当x是3的倍数时，x ◎ y = (y * x)；
其他情况下，x ◎ y = y + x ** 4。
和 ⊙，规则如下：
当x是5的倍数时，x ⊙ y = x ◎ y；
其他情况下，x ⊙ y = x * x / y。
运算优先级：** = ⊙ > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 / 6 + 9 ⊙ 9 ◎ 9
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◎，规则如下：\n当x是3的倍数时，x ◎ y = (y * x)；\n其他情况下，x ◎ y = y + x ** 4。\n和 ⊙，规则如下：\n当x是5的倍数时，x ⊙ y = x ◎ y；\n其他情况下，x ⊙ y = x * x / y。\n运算优先级：** = ⊙ > * = / = % > + = - = ◎。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 6 / 6 + 9 ⊙ 9 ◎ 9\n请将最终答案填入\\boxed{}中。"
},
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],
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},
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"▽": null,
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"○": null,
"◎": {
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"conditions": [
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],
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},
"☆": null,
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"♢": null
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"seed": 43166889,
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logic-v2 | Define △, the rules are as follows:
when the sum of x and y is odd, x △ y = x - x / y * 5 * x;
otherwise, x △ y = x - y - y - x * x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7
Please fill your final answer in \boxed{}. | {
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},
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"⊗": null,
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"□": null,
"△": {
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"conditions": [
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"operation": " x - x / y * 5 * x"
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"○": null,
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logic-v2 | 定义 △，规则如下：
实数域上，x △ y = x + y。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 / 8 / 7 △ 6
请将最终答案填入\boxed{}中。 | {
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},
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"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
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"♡": null,
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"seed": 26766019,
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logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y * y + (x) / y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y - x - y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y ⊕ x - x + x.
The precedence of operations: ** > * = / = % = ♡ > + = - = ♢ = ⊕。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ♢ 4 ♡ 8 ** 2 ⊕ 8
Please fill your final answer in \boxed{}. | {
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"△": null,
"▽": null,
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"conditions": [],
"default_operation": " y ⊕ x - x + x",
"precedence": 2
},
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"associativity": "left",
"conditions": [],
"default_operation": " y * y + (x) / y",
"precedence": 1
}
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"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = y * y + (x) / y.\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = y - x - y.\nand ♡, the rules are as follows:\non the real number field, x ♡ y = y ⊕ x - x + x.\nThe precedence of operations: ** > * = / = % = ♡ > + = - = ♢ = ⊕。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 ♢ 4 ♡ 8 ** 2 ⊕ 8\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define □, the rules are as follows:
when y is a multiple of 3, x □ y = y * x - x + x;
otherwise, x □ y = y - y - y * x - x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y / x + y + x.
The precedence of operations: □ > ** = ⊗ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 / 6 ⊗ 3 % 1 □ 8
Please fill your final answer in \boxed{}. | {
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"question": "Define □, the rules are as follows:\nwhen y is a multiple of 3, x □ y = y * x - x + x;\notherwise, x □ y = y - y - y * x - x.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = y / x + y + x.\nThe precedence of operations: □ > ** = ⊗ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 8 / 6 ⊗ 3 % 1 □ 8\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 □，规则如下：
当x等于y时，x □ y = 5 - x ** y + x * y；
其他情况下，x □ y = abs(x - y + x - y) + x。
和 ☆，规则如下：
当y是5的倍数时，x ☆ y = x / y * (x - x * y)；
其他情况下，x ☆ y = x - y - x + x - y。
运算优先级：□ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ☆ 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 □，规则如下：\n当x等于y时，x □ y = 5 - x ** y + x * y；\n其他情况下，x □ y = abs(x - y + x - y) + x。\n和 ☆，规则如下：\n当y是5的倍数时，x ☆ y = x / y * (x - x * y)；\n其他情况下，x ☆ y = x - y - x + x - y。\n运算优先级：□ > ** > * = / = % = ☆ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ☆ 10\n请将最终答案填入\\boxed{}中。"
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logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = (y + x) * y ** 1.
and ⊗, the rules are as follows:
when x is equal to y, x ⊗ y = y - y * x - y;
otherwise, x ⊗ y = x ** abs(y + x) * x.
The precedence of operations: ⊗ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ⊗ 7 + 7 □ 2 ** 6
Please fill your final answer in \boxed{}. | {
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"question": "Define □, the rules are as follows:\non the real number field, x □ y = (y + x) * y ** 1.\nand ⊗, the rules are as follows:\nwhen x is equal to y, x ⊗ y = y - y * x - y;\notherwise, x ⊗ y = x ** abs(y + x) * x.\nThe precedence of operations: ⊗ > ** > * = / = % = □ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 1 ⊗ 7 + 7 □ 2 ** 6\nPlease fill your final answer in \\boxed{}."
},
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"seed": 22074320,
"simplified_expr": "((( 1 ** abs(7 + 1) * 1)) + (( (((2 ** 6)) + 7) * ((2 ** 6)) ** 1)))",
"solutions_count": null,
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"seed": 22074320,
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} |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y * x * y - 3 - y.
and △, the rules are as follows:
on the real number field, x △ y = 2 * y ♡ x.
The precedence of operations: ** > * = / = % = ♡ = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 8 - 7 ♡ 9
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | 定义 ○，规则如下：
当x小于y时，x ○ y = y + x * x；
其他情况下，x ○ y = y * x - 4。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ○ 7 ○ 1
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ▽，规则如下：
当x和y都是奇数时，x ▽ y = x - y * y / x；
其他情况下，x ▽ y = x + y * y - x / y。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 - 6 ▽ 1 ** 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ▽，规则如下：\n当x和y都是奇数时，x ▽ y = x - y * y / x；\n其他情况下，x ▽ y = x + y * y - x / y。\n运算优先级：** > * = / = % > + = - = ▽。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 - 6 ▽ 1 ** 4\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y + 2 ** x + y - y。
和 ☆，规则如下：
当x等于y时，x ☆ y = 1 * 1 * y * x ▽ 2；
其他情况下，x ☆ y = y + y - 1 ▽ x。
和 ⊕，规则如下：
实数域上，x ⊕ y = y - (x + y + 2 * y)。
运算优先级：▽ = ⊕ > ** > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ☆ 3 ⊕ 9 / 5 ▽ 6
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ▽，规则如下：\n实数域上，x ▽ y = y + 2 ** x + y - y。\n和 ☆，规则如下：\n当x等于y时，x ☆ y = 1 * 1 * y * x ▽ 2；\n其他情况下，x ☆ y = y + y - 1 ▽ x。\n和 ⊕，规则如下：\n实数域上，x ⊕ y = y - (x + y + 2 * y)。\n运算优先级：▽ = ⊕ > ** > * = / = % > + = - = ☆。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 6 ☆ 3 ⊕ 9 / 5 ▽ 6\n请将最终答案填入\\boxed{}中。"
},
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"seed": 61637526,
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} |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y * x - 2 + y - x.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 △ 6
Please fill your final answer in \boxed{}. | {
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} |
logic-v2 | 定义 ◇，规则如下：
当y是3的倍数时，x ◇ y = x * y + y；
其他情况下，x ◇ y = x / y。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◇，规则如下：\n当y是3的倍数时，x ◇ y = x * y + y；\n其他情况下，x ◇ y = x / y。\n运算优先级：◇ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 7\n请将最终答案填入\\boxed{}中。"
},
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"◇": {
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} |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = x * y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * y + y.
The precedence of operations: ** > * = / = % = ♡ > + = - = ⊕。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ♡ 9 % 6 ♡ 6 ⊕ 1
Please fill your final answer in \boxed{}. | {
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},
"target": null,
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"question": "Define ♡, the rules are as follows:\non the real number field, x ♡ y = x * y.\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = x * y + y.\nThe precedence of operations: ** > * = / = % = ♡ > + = - = ⊕。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ♡ 9 % 6 ♡ 6 ⊕ 1\nPlease fill your final answer in \\boxed{}."
},
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"seed": 15801642,
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"task_type": "operation"
} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x * y - y / y - y.
and □, the rules are as follows:
on the real number field, x □ y = y * x * 3 - 1 ** x.
and ☆, the rules are as follows:
when the sum of x and y is odd, x ☆ y = y ** x / x;
otherwise, x ☆ y = x - x * y.
The precedence of operations: ♢ > ** > * = / = % = □ > + = - = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 □ 4 ♢ 7 ☆ 7
Please fill your final answer in \boxed{}. | {
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"operation": " y ** x / x"
}
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"precedence": 1
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
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}
},
"target": null,
"total_length": null,
"trace_id": "bb6a3a58-8fce-43c9-82c3-130268aaf751"
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"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = x * y - y / y - y.\nand □, the rules are as follows:\non the real number field, x □ y = y * x * 3 - 1 ** x.\nand ☆, the rules are as follows:\nwhen the sum of x and y is odd, x ☆ y = y ** x / x;\notherwise, x ☆ y = x - x * y.\nThe precedence of operations: ♢ > ** > * = / = % = □ > + = - = ☆。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 □ 4 ♢ 7 ☆ 7\nPlease fill your final answer in \\boxed{}."
},
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
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"conditions": [
{
"condition": "x和y的和是奇数",
"operation": " y ** x / x"
}
],
"default_operation": " x - x * y",
"precedence": 1
},
"♡": null,
"♢": {
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"conditions": [],
"default_operation": " x * y - y / y - y",
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},
"target": null,
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"seed": 13645820,
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} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x + abs(x + 1) * y.
and ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = 3 - y ◎ x + y;
otherwise, x ▽ y = y + 1 + x + x.
The precedence of operations: ** = ◎ > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ▽ 5 ◎ 8
Please fill your final answer in \boxed{}. | {
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"precedence": 2
},
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " x + abs(x + 1) * y",
"precedence": 3
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "65d29932-1d53-422d-afbf-1068e6bc204f"
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = x + abs(x + 1) * y.\nand ▽, the rules are as follows:\nwhen the sum of x and y is even, x ▽ y = 3 - y ◎ x + y;\notherwise, x ▽ y = y + 1 + x + x.\nThe precedence of operations: ** = ◎ > * = / = % = ▽ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 8 ▽ 5 ◎ 8\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x + y.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ** 1 △ 9
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y + abs(x) * x / x。
和 ⊙，规则如下：
当y是3的倍数时，x ⊙ y = x / y ⊕ x ** y；
其他情况下，x ⊙ y = 4 * x + (y / y)。
和 □，规则如下：
当x是偶数时，x □ y = y + 5 * y ⊙ x；
其他情况下，x □ y = x * y ⊕ y。
运算优先级：⊕ > ** > * = / = % = ⊙ > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 □ 4 ⊙ 5 ⊕ 7
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ⊕, the rules are as follows:
when y is a multiple of 5, x ⊕ y = 1 + y * x;
otherwise, x ⊕ y = x / y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y * x / y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x / x ** (y).
The precedence of operations: ⊕ > ** > * = / = % > + = - = ◇ = ♡。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ♡ 7 ◇ 2
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define ⊕, the rules are as follows:
when x and y are both even, x ⊕ y = x * (y) + x / y;
otherwise, x ⊕ y = y + 2 ** x - y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y * (y) ⊕ x + y.
and ◎, the rules are as follows:
when x is a multiple of 3, x ◎ y = x + x + 5 + y;
otherwise, x ◎ y = y ⊕ (y / x ** 4).
The precedence of operations: ☆ = ◎ > ** > * = / = % = ⊕ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ☆ 1 ◎ 1 ⊕ 5
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = (y - 1 * 5) + x。
运算优先级：** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ** 5 ○ 7
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = 5 - y - y + x - 3.
and ○, the rules are as follows:
when x is less than y, x ○ y = y + x;
otherwise, x ○ y = x - y - x - x ◎ x.
The precedence of operations: ○ > ** > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ○ 10
Please fill your final answer in \boxed{}. | {
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " y + x"
}
],
"default_operation": " x - y - x - x ◎ x",
"precedence": 4
},
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " 5 - y - y + x - 3",
"precedence": 2
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "9aa0da14-acf6-45c8-9a31-6769ba887931"
},
"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = 5 - y - y + x - 3.\nand ○, the rules are as follows:\nwhen x is less than y, x ○ y = y + x;\notherwise, x ○ y = x - y - x - x ◎ x.\nThe precedence of operations: ○ > ** > * = / = % = ◎ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ○ 10\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
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"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 75217342,
"simplified_expr": "( 10 + 3)",
"solutions_count": null,
"symbol_definitions": {
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " y + x"
}
],
"default_operation": " x - y - x - x ◎ x",
"precedence": 4
},
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " 5 - y - y + x - 3",
"precedence": 2
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "9aa0da14-acf6-45c8-9a31-6769ba887931"
},
"seed": 75217342,
"task_id": 275217342,
"task_type": "operation"
} |
logic-v2 | 定义 ○，规则如下：
当x等于y时，x ○ y = y - x * x - x / y；
其他情况下，x ○ y = y - x * y / x + y。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 58469801,
"simplified_expr": "2",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "x等于y",
"operation": " y - x * x - x / y"
}
],
"default_operation": " y - x * y / x + y",
"precedence": 1
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "83ce1c23-c1c4-4b66-884e-bd27c8ec3070"
},
"question": "定义 ○，规则如下：\n当x等于y时，x ○ y = y - x * x - x / y；\n其他情况下，x ○ y = y - x * y / x + y。\n运算优先级：** > * = / = % > + = - = ○。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 58469801,
"simplified_expr": "2",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " y - x * x - x / y"
}
],
"default_operation": " y - x * y / x + y",
"precedence": 1
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "83ce1c23-c1c4-4b66-884e-bd27c8ec3070"
},
"seed": 58469801,
"task_id": 258469801,
"task_type": "operation"
} |
logic-v2 | Define □, the rules are as follows:
when x is equal to y, x □ y = abs(y * y) * x / x;
otherwise, x □ y = 5 - y + y - x.
and ◇, the rules are as follows:
when y is odd, x ◇ y = 3 - x □ 3 / y;
otherwise, x ◇ y = y / y * x.
The precedence of operations: □ > ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 □ 10
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 50760581,
"simplified_expr": "( 5 - 10 + 10 - 6)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " abs(y * y) * x / x"
}
],
"default_operation": " 5 - y + y - x",
"precedence": 5
},
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " 3 - x □ 3 / y"
}
],
"default_operation": " y / y * x",
"precedence": 1
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "195b3f20-ea05-4a88-a485-d0a1793efe1f"
},
"question": "Define □, the rules are as follows:\nwhen x is equal to y, x □ y = abs(y * y) * x / x;\notherwise, x □ y = 5 - y + y - x.\nand ◇, the rules are as follows:\nwhen y is odd, x ◇ y = 3 - x □ 3 / y;\notherwise, x ◇ y = y / y * x.\nThe precedence of operations: □ > ** > * = / = % > + = - = ◇。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 □ 10\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "6 □ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 50760581,
"simplified_expr": "( 5 - 10 + 10 - 6)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " abs(y * y) * x / x"
}
],
"default_operation": " 5 - y + y - x",
"precedence": 5
},
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " 3 - x □ 3 / y"
}
],
"default_operation": " y / y * x",
"precedence": 1
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "195b3f20-ea05-4a88-a485-d0a1793efe1f"
},
"seed": 50760581,
"task_id": 250760581,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x - y + x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y * x * y.
The precedence of operations: ☆ > ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ◇ 1 ☆ 8
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-62",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 1 ☆ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 26913740,
"simplified_expr": "( 1 - (( 8 * 1 * 8)) + 1)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y + x",
"precedence": 1
},
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " y * x * y",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "80776e7b-a8ef-45db-9718-f014d775a703"
},
"question": "Define ◇, the rules are as follows:\non the real number field, x ◇ y = x - y + x.\nand ☆, the rules are as follows:\non the real number field, x ☆ y = y * x * y.\nThe precedence of operations: ☆ > ** > * = / = % > + = - = ◇。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 1 ◇ 1 ☆ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 1 ☆ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 26913740,
"simplified_expr": "( 1 - (( 8 * 1 * 8)) + 1)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y + x",
"precedence": 1
},
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " y * x * y",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "80776e7b-a8ef-45db-9718-f014d775a703"
},
"seed": 26913740,
"task_id": 226913740,
"task_type": "operation"
} |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x * y - 2 / x ** y。
运算优先级：** > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 % 3 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 % 3 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 84654179,
"simplified_expr": "( ((10 % 3)) * 5 - 2 / ((10 % 3)) ** 5)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y - 2 / x ** y",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "9c84a7c9-71a6-4242-b370-e6325bf682ee"
},
"question": "定义 ♢，规则如下：\n实数域上，x ♢ y = x * y - 2 / x ** y。\n运算优先级：** > * = / = % > + = - = ♢。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 % 3 ♢ 5\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "10 % 3 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 84654179,
"simplified_expr": "( ((10 % 3)) * 5 - 2 / ((10 % 3)) ** 5)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y - 2 / x ** y",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "9c84a7c9-71a6-4242-b370-e6325bf682ee"
},
"seed": 84654179,
"task_id": 284654179,
"task_type": "operation"
} |
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