env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ⊕，规则如下：
当x小于y时，x ⊕ y = y + x；
其他情况下，x ⊕ y = y ** y - x。
和 ◎，规则如下：
当y是偶数时，x ◎ y = x ⊕ y - y；
其他情况下，x ◎ y = x * y + 4。
和 □，规则如下：
实数域上，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: 9 □ 3 ⊕ 2
请将最终答案填入\boxed{}中。 | {
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"numbers": null,
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"seed": 6532255,
"simplified_expr": "( 9 * (( 2 ** 2 - 3)) ** 9)",
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"symbol_definitions": {
"⊕": {
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],
"default_operation": " y ** y - x",
"precedence": 3
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"⊗": null,
"⊙": null,
"□": {
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"conditions": [],
"default_operation": " x * y ** x",
"precedence": 1
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "y是偶数",
"operation": " x ⊕ y - y"
}
],
"default_operation": " x * y + 4",
"precedence": 1
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "4291a7fa-3ad5-4201-b7fa-b2cb7dbbf2a0"
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"question": "定义 ⊕，规则如下：\n当x小于y时，x ⊕ y = y + x；\n其他情况下，x ⊕ y = y ** y - x。\n和 ◎，规则如下：\n当y是偶数时，x ◎ y = x ⊕ y - y；\n其他情况下，x ◎ y = x * y + 4。\n和 □，规则如下：\n实数域上，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: 9 □ 3 ⊕ 2\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "9 □ 3 ⊕ 2",
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"numbers": null,
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"seed": 6532255,
"simplified_expr": "( 9 * (( 2 ** 2 - 3)) ** 9)",
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"symbol_definitions": {
"⊕": {
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"conditions": [
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"operation": " y + x"
}
],
"default_operation": " y ** y - x",
"precedence": 3
},
"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y ** x",
"precedence": 1
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [
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"operation": " x ⊕ y - y"
}
],
"default_operation": " x * y + 4",
"precedence": 1
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "4291a7fa-3ad5-4201-b7fa-b2cb7dbbf2a0"
},
"seed": 6532255,
"task_id": 206532255,
"task_type": "operation"
} |
logic-v2 | 定义 △，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: 4
请将最终答案填入\boxed{}中。 | {
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"answer": "4",
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"expression": "4",
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"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
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"seed": 93733731,
"simplified_expr": "4",
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"symbol_definitions": {
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"⊙": null,
"□": null,
"△": {
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"default_operation": " y + x + y",
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},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "6aa8ca14-f3c4-4455-9570-df8e6c608bf0"
},
"question": "定义 △，规则如下：\n实数域上，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: 4\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "4",
"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": 93733731,
"simplified_expr": "4",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x + y",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "6aa8ca14-f3c4-4455-9570-df8e6c608bf0"
},
"seed": 93733731,
"task_id": 293733731,
"task_type": "operation"
} |
logic-v2 | 定义 ♢，规则如下：
当x是偶数时，x ♢ y = (y * y) - x；
其他情况下，x ♢ y = y * x。
和 ◇，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 * 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 ◎ 1 ** 5 ◇ 4 ♢ 7
请将最终答案填入\boxed{}中。 | {
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"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 1 ** 5 ◇ 4 ♢ 7",
"fill_length": null,
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"num_of_numbers": null,
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"operators": null,
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"seed": 5883345,
"simplified_expr": "( 7 * (((( 4 * 1 / 1)) ** (( 5 / 4 - 5)))))",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
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"△": null,
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"conditions": [],
"default_operation": " x / y - x",
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},
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y / y",
"precedence": 5
},
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " (y * y) - x"
}
],
"default_operation": " y * x",
"precedence": 3
}
},
"target": null,
"total_length": null,
"trace_id": "2a829e91-a71c-495d-95c2-b7721505a0fd"
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"question": "定义 ♢，规则如下：\n当x是偶数时，x ♢ y = (y * y) - x；\n其他情况下，x ♢ y = y * x。\n和 ◇，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 * 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 ◎ 1 ** 5 ◇ 4 ♢ 7\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 1 ** 5 ◇ 4 ♢ 7",
"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": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 5883345,
"simplified_expr": "( 7 * (((( 4 * 1 / 1)) ** (( 5 / 4 - 5)))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x / y - x",
"precedence": 5
},
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y / y",
"precedence": 5
},
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " (y * y) - x"
}
],
"default_operation": " y * x",
"precedence": 3
}
},
"target": null,
"total_length": null,
"trace_id": "2a829e91-a71c-495d-95c2-b7721505a0fd"
},
"seed": 5883345,
"task_id": 205883345,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = 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: 8 ▽ 9 ▽ 7 * 9
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-108",
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"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 9 ▽ 7 * 9",
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"seed": 53478854,
"simplified_expr": "((( (( 8 - (5 + 9 + 8))) - (5 + 7 + (( 8 - (5 + 9 + 8)))))) * 9)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
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"△": null,
"▽": {
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"default_operation": " x - (5 + y + x)",
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},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "24405a46-0302-4dfb-8dc6-453b62763a30"
},
"question": "Define ▽, the rules are as follows:\non the real number field, x ▽ y = 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: 8 ▽ 9 ▽ 7 * 9\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 9 ▽ 7 * 9",
"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": 53478854,
"simplified_expr": "((( (( 8 - (5 + 9 + 8))) - (5 + 7 + (( 8 - (5 + 9 + 8)))))) * 9)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " x - (5 + y + x)",
"precedence": 4
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "24405a46-0302-4dfb-8dc6-453b62763a30"
},
"seed": 53478854,
"task_id": 253478854,
"task_type": "operation"
} |
logic-v2 | 定义 ♡，规则如下：
当x大于y时，x ♡ y = 5 * 5 + x + y + 5；
其他情况下，x ♡ y = 4 * x + y ** x * 4。
和 ⊙，规则如下：
当x和y都是奇数时，x ⊙ y = y ♡ x ** x + y；
其他情况下，x ⊙ y = y + (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: 9 ♡ 7 ⊙ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "88",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 7 ⊙ 4",
"fill_length": null,
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"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
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"numbers": null,
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"question_sequence": null,
"seed": 48834581,
"simplified_expr": "( 4 + ((( 5 * 5 + 9 + 7 + 5)) - 4) - 4 + (( 5 * 5 + 9 + 7 + 5)))",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
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"conditions": [
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"condition": "x和y都是奇数",
"operation": " y ♡ x ** x + y"
}
],
"default_operation": " y + (x - y) - y + x",
"precedence": 2
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " 5 * 5 + x + y + 5"
}
],
"default_operation": " 4 * x + y ** x * 4",
"precedence": 5
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "3aed1751-d73f-444b-af40-09bdb83dc187"
},
"question": "定义 ♡，规则如下：\n当x大于y时，x ♡ y = 5 * 5 + x + y + 5；\n其他情况下，x ♡ y = 4 * x + y ** x * 4。\n和 ⊙，规则如下：\n当x和y都是奇数时，x ⊙ y = y ♡ x ** x + y；\n其他情况下，x ⊙ y = y + (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: 9 ♡ 7 ⊙ 4\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 7 ⊙ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 48834581,
"simplified_expr": "( 4 + ((( 5 * 5 + 9 + 7 + 5)) - 4) - 4 + (( 5 * 5 + 9 + 7 + 5)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " y ♡ x ** x + y"
}
],
"default_operation": " y + (x - y) - y + x",
"precedence": 2
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " 5 * 5 + x + y + 5"
}
],
"default_operation": " 4 * x + y ** x * 4",
"precedence": 5
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "3aed1751-d73f-444b-af40-09bdb83dc187"
},
"seed": 48834581,
"task_id": 248834581,
"task_type": "operation"
} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y - abs(x) * 2 - x.
and ☆, the rules are as follows:
when x is less than y, x ☆ y = x - y - y - x;
otherwise, x ☆ y = (x ♢ y).
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x ☆ 5 - 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 ♢ 7 ☆ 2
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-35",
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"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 6 ♢ 7 ☆ 2",
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"n_types": null,
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"seed": 30005420,
"simplified_expr": "( ((( 2 - abs(7) * 2 - 7))) - abs(((((( 2 - 5 - 5 - 2)) - 6)))) * 2 - ((((( 2 - 5 - 5 - 2)) - 6))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
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"precedence": 1
},
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " x - y - y - x"
}
],
"default_operation": " (x ♢ y)",
"precedence": 3
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y - abs(x) * 2 - x",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "a1f47d64-bc9b-4eb5-8b85-bce5771da8db"
},
"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = y - abs(x) * 2 - x.\nand ☆, the rules are as follows:\nwhen x is less than y, x ☆ y = x - y - y - x;\notherwise, x ☆ y = (x ♢ y).\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = x ☆ 5 - 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 ⊕ 6 ♢ 7 ☆ 2\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 6 ♢ 7 ☆ 2",
"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": 30005420,
"simplified_expr": "( ((( 2 - abs(7) * 2 - 7))) - abs(((((( 2 - 5 - 5 - 2)) - 6)))) * 2 - ((((( 2 - 5 - 5 - 2)) - 6))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
"associativity": "left",
"conditions": [],
"default_operation": " x ☆ 5 - y",
"precedence": 1
},
"⊗": null,
"⊙": null,
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logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = 5 / x - 1 - y。
和 ◇，规则如下：
当x等于y时，x ◇ y = x - x - y + 2 / x；
其他情况下，x ◇ y = x ♢ y - 5 - 1 ** x。
和 ⊕，规则如下：
实数域上，x ⊕ y = abs(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 ◇ 1 ♢ 8 ◇ 6 ⊕ 5
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：
实数域上，x ⊗ y = x / x + y。
和 △，规则如下：
当x和y的和是奇数时，x △ y = x * x + y；
其他情况下，x △ y = (y * y ** x)。
和 ♡，规则如下：
当x是3的倍数时，x ♡ y = abs(y) * x * y；
其他情况下，x ♡ y = 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: 2 △ 3 ♡ 9 ⊗ 6
请将最终答案填入\boxed{}中。 | {
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"♢": null
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = x / x + y。\n和 △，规则如下：\n当x和y的和是奇数时，x △ y = x * x + y；\n其他情况下，x △ y = (y * y ** x)。\n和 ♡，规则如下：\n当x是3的倍数时，x ♡ y = abs(y) * x * y；\n其他情况下，x ♡ y = 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: 2 △ 3 ♡ 9 ⊗ 6\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.
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
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.\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\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 + y - abs(y) - x.
and ◎, the rules are as follows:
when y is even, x ◎ y = y / 5 / 4 ⊕ x * y;
otherwise, x ◎ y = y - y ⊕ y / x.
and ○, the rules are as follows:
on the real number field, x ○ y = y - x ⊕ 1 - 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 ○ 5 ◎ 5 ** 1 ⊕ 6
Please fill your final answer in \boxed{}. | {
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},
"◎": {
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"operation": " y / 5 / 4 ⊕ x * y"
}
],
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},
"☆": null,
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},
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},
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}
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = 2 + x + (y + x)。
和 ☆，规则如下：
实数域上，x ☆ y = y ** x * 3 ⊕ x + y。
和 ◎，规则如下：
当x是5的倍数时，x ◎ y = y * y / x / 5；
其他情况下，x ◎ y = abs(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 ◎ 5 + 3 ☆ 9 + 3 ⊕ 8
请将最终答案填入\boxed{}中。 | {
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"conditions": [
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"condition": "x是5的倍数",
"operation": " y * y / x / 5"
}
],
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},
"☆": {
"associativity": "left",
"conditions": [],
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"precedence": 1
},
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"♢": null
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"question": "定义 ⊕，规则如下：\n实数域上，x ⊕ y = 2 + x + (y + x)。\n和 ☆，规则如下：\n实数域上，x ☆ y = y ** x * 3 ⊕ x + y。\n和 ◎，规则如下：\n当x是5的倍数时，x ◎ y = y * y / x / 5；\n其他情况下，x ◎ y = abs(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: 5 ◎ 5 + 3 ☆ 9 + 3 ⊕ 8\n请将最终答案填入\\boxed{}中。"
},
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"seed": 23145102,
"simplified_expr": "(((((( 2 + ((((9 ** ((((((((5 * 5)) / 5)) / 5)) + 3)))) * 3)) + (((((((((5 * 5)) / 5)) / 5)) + 3)) + ((((9 ** ((((((((5 * 5)) / 5)) / 5)) + 3)))) * 3))))) + 9))) + (( 2 + 3 + (8 + 3))))",
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"operation": " y * y / x / 5"
}
],
"default_operation": " abs(x / y / y)",
"precedence": 4
},
"☆": {
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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 = 3 - (x / 4) + y;
otherwise, x ⊗ y = y + (y - x + y) ** y.
and ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = abs(x + y) - 3 + x;
otherwise, x ▽ y = x / x / x - y - y.
and ⊙, the rules are as follows:
when x is odd, x ⊙ y = (x * x + 5 - y) * y;
otherwise, x ⊙ y = x - x * abs(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 ▽ 10 ⊙ 10 ⊗ 1
Please fill your final answer in \boxed{}. | {
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},
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}
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"default_operation": " y + (y - x + y) ** y",
"precedence": 2
},
"⊙": {
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"operation": " (x * x + 5 - y) * y"
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],
"default_operation": " x - x * abs(y + x)",
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logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x + y + 1 + 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 % 6 ▽ 2
Please fill your final answer in \boxed{}. | {
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},
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"conditions": [],
"default_operation": " x + y + 1 + y",
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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。
和 ♢，规则如下：
实数域上，x ♢ y = y - (x ⊙ x)。
和 ◎，规则如下：
当x是3的倍数时，x ◎ y = abs(x * 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: 8 ♢ 4 ◎ 3 - 6 ⊙ 8
请将最终答案填入\boxed{}中。 | {
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],
"default_operation": " x * y - x",
"precedence": 3
},
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y - (x ⊙ x)",
"precedence": 2
}
},
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"question": "定义 ⊙，规则如下：\n实数域上，x ⊙ y = x / y。\n和 ♢，规则如下：\n实数域上，x ♢ y = y - (x ⊙ x)。\n和 ◎，规则如下：\n当x是3的倍数时，x ◎ y = abs(x * 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: 8 ♢ 4 ◎ 3 - 6 ⊙ 8\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "8 ♢ 4 ◎ 3 - 6 ⊙ 8",
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],
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}
},
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"seed": 14044134,
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logic-v2 | 定义 □，规则如下：
当x和y都是偶数时，x □ y = x - x + y；
其他情况下，x □ y = 5 * x - y / x。
和 △，规则如下：
当x等于y时，x △ y = x - x - y；
其他情况下，x △ y = y / x + 5。
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 △ 3 □ 3
请将最终答案填入\boxed{}中。 | {
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"♢": null
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"question": "定义 □，规则如下：\n当x和y都是偶数时，x □ y = x - x + y；\n其他情况下，x □ y = 5 * x - y / x。\n和 △，规则如下：\n当x等于y时，x △ y = x - x - y；\n其他情况下，x △ y = y / x + 5。\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 △ 3 □ 3\n请将最终答案填入\\boxed{}中。"
},
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"seed": 68233480,
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} |
logic-v2 | 定义 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = abs(x * y + y)；
其他情况下，x ⊕ y = x * 2 * (y)。
和 ☆，规则如下：
当x等于y时，x ☆ y = abs(x) + y；
其他情况下，x ☆ y = 2 * x - 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 ⊕ 3 ☆ 10 ☆ 2 ⊙ 9
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5的倍数时，x ⊕ y = y - x / y；
其他情况下，x ⊕ y = x + x + y。
和 ♡，规则如下：
实数域上，x ♡ y = (y / x) - x。
和 ▽，规则如下：
当x和y都是偶数时，x ▽ y = y + y - x；
其他情况下，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: 7 ⊕ 7 ▽ 4 ♡ 7
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 a multiple of 5, x △ y = 4 - y + x + x;
otherwise, x △ y = x - 5 + 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
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ○，规则如下：
当x是5的倍数时，x ○ y = y / abs(x) - y * x - y；
其他情况下，x ○ y = y * x - 3 + 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 ○ 7 / 4
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 / y。
和 △，规则如下：
实数域上，x △ y = (x ♢ y)。
和 ♡，规则如下：
实数域上，x ♡ y = 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: 1 ♢ 10 △ 1 ♡ 8
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.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (x + x ** 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: 6 ♢ 7 □ 2
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ⊕，规则如下：
当x和y的和是偶数时，x ⊕ y = x + y；
其他情况下，x ⊕ y = y * y + x。
和 △，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)。
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 ⊗ 10 ⊕ 5 △ 5
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 * y.
and ⊕, the rules are as follows:
when x is greater than y, x ⊕ y = x - y * y;
otherwise, x ⊕ y = x - 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: 9 ♡ 1 ⊙ 9
Please fill your final answer in \boxed{}. | {
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"precedence": 5
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"♢": null
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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 * y.\nand ⊕, the rules are as follows:\nwhen x is greater than y, x ⊕ y = x - y * y;\notherwise, x ⊕ y = x - 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: 9 ♡ 1 ⊙ 9\nPlease fill your final answer in \\boxed{}."
},
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"symbol_definitions": {
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"○": null,
"◎": null,
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"♡": {
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"precedence": 5
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logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x - y + 2 - x。
和 ▽，规则如下：
实数域上，x ▽ y = x + 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: 10 ♡ 10 ▽ 4 ♡ 9
请将最终答案填入\boxed{}中。 | {
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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 + 2 - x。\n和 ▽，规则如下：\n实数域上，x ▽ y = x + 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: 10 ♡ 10 ▽ 4 ♡ 9\n请将最终答案填入\\boxed{}中。"
},
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"seed": 4757686,
"simplified_expr": "( (( 10 - (((((10 + (((( 10 - 4 + 2 - 10)) * 10)))) + 4))) + 2 - 10)) - 9 + 2 - (( 10 - (((((10 + (((( 10 - 4 + 2 - 10)) * 10)))) + 4))) + 2 - 10)))",
"solutions_count": null,
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"conditions": [],
"default_operation": " x + x ♡ y * x + y",
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},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
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"conditions": [],
"default_operation": " x - y + 2 - x",
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},
"♢": null
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"seed": 4757686,
"task_id": 204757686,
"task_type": "operation"
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logic-v2 | Define ♡, the rules are as follows:
on the real number field, 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: 6 ⊙ 5
Please fill your final answer in \boxed{}. | {
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
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} |
logic-v2 | 定义 ⊙，规则如下：
当x和y的和是奇数时，x ⊙ y = y * x - y；
其他情况下，x ⊙ y = y - x - x。
和 ◇，规则如下：
实数域上，x ◇ y = y + y - x。
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: 7 □ 9 ◇ 10 ⊙ 3
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的和是奇数时，x ⊙ y = y * x - y；\n其他情况下，x ⊙ y = y - x - x。\n和 ◇，规则如下：\n实数域上，x ◇ y = y + y - x。\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: 7 □ 9 ◇ 10 ⊙ 3\n请将最终答案填入\\boxed{}中。"
},
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"expression": "7 □ 9 ◇ 10 ⊙ 3",
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"operation": " y * x - y"
}
],
"default_operation": " y - x - x",
"precedence": 1
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"□": {
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"conditions": [],
"default_operation": " x + x / x + y",
"precedence": 4
},
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " y + y - x",
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},
"○": null,
"◎": null,
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"♡": null,
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logic-v2 | Define ⊙, the rules are as follows:
when the sum of x and y is even, x ⊙ y = 1 + y * x;
otherwise, x ⊙ y = x - x + y + x + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = 1 - x - y / y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 4 - 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: 7 ⊗ 4 ◇ 6 ⊙ 6
Please fill your final answer in \boxed{}. | {
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"conditions": [
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"condition": "x和y的和是偶数",
"operation": " 1 + y * x"
}
],
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"precedence": 3
},
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " 4 - x ⊙ y + x / x",
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},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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},
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"solutions_count": null,
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"⊙": {
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"conditions": [
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"condition": "x和y的和是偶数",
"operation": " 1 + y * x"
}
],
"default_operation": " x - x + y + x + x",
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},
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " 4 - x ⊙ y + x / x",
"precedence": 5
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"seed": 20340027,
"task_id": 220340027,
"task_type": "operation"
} |
logic-v2 | 定义 ◇，规则如下：
当y是5的倍数时，x ◇ y = x - x - y - y；
其他情况下，x ◇ y = x / y。
和 ☆，规则如下：
实数域上，x ☆ y = 3 + y * (x)。
和 ◎，规则如下：
当y是5的倍数时，x ◎ y = 3 ☆ x / y - y；
其他情况下，x ◎ y = x + 1 ☆ 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: 2 ☆ 3 - 3 ◇ 8 - 6 ◎ 7
请将最终答案填入\boxed{}中。 | {
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},
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"question": "定义 ◇，规则如下：\n当y是5的倍数时，x ◇ y = x - x - y - y；\n其他情况下，x ◇ y = x / y。\n和 ☆，规则如下：\n实数域上，x ☆ y = 3 + y * (x)。\n和 ◎，规则如下：\n当y是5的倍数时，x ◎ y = 3 ☆ x / y - y；\n其他情况下，x ◎ y = x + 1 ☆ 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: 2 ☆ 3 - 3 ◇ 8 - 6 ◎ 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 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.
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: 5 ▽ 4 □ 4 ▽ 7 * 4 ⊗ 3
Please fill your final answer in \boxed{}. | {
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"conditions": [],
"default_operation": " y ⊗ x",
"precedence": 3
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"♢": null
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"target": null,
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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.\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: 5 ▽ 4 □ 4 ▽ 7 * 4 ⊗ 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "5 ▽ 4 □ 4 ▽ 7 * 4 ⊗ 3",
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"seed": 10742148,
"simplified_expr": "((( ((( (5 * 4) + 5))) + (((( (4 * 7) + 4))) - ((( (4 * 7) + 4)))))) * (( (3 * 4) + 3)))",
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"conditions": [],
"default_operation": " x + (y - y)",
"precedence": 2
},
"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " y ⊗ x",
"precedence": 3
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "e46033ab-79a4-4002-9559-b0bea5821d19"
},
"seed": 10742148,
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logic-v2 | 定义 ◎，规则如下：
当x和y的和是偶数时，x ◎ y = x * x / y；
其他情况下，x ◎ y = y / abs(x)。
和 ⊕，规则如下：
实数域上，x ⊕ y = 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: 2 ◎ 2 ⊕ 6
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的和是偶数时，x ◎ y = x * x / y；\n其他情况下，x ◎ y = y / abs(x)。\n和 ⊕，规则如下：\n实数域上，x ⊕ y = 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: 2 ◎ 2 ⊕ 6\n请将最终答案填入\\boxed{}中。"
},
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"seed": 87779391,
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} |
logic-v2 | 定义 □，规则如下：
当x是奇数时，x □ y = x - x + y；
其他情况下，x □ y = y * 4 + x * 1。
和 ◎，规则如下：
当x和y都是奇数时，x ◎ y = (x / 4 - y)；
其他情况下，x ◎ y = 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: 5 □ 5 ◎ 8 + 1
请将最终答案填入\boxed{}中。 | {
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"☆": null,
"♡": null,
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"target": null,
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"trace_id": "87f465a6-c68f-44a9-bc00-a3b50406a6c1"
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"question": "定义 □，规则如下：\n当x是奇数时，x □ y = x - x + y；\n其他情况下，x □ y = y * 4 + x * 1。\n和 ◎，规则如下：\n当x和y都是奇数时，x ◎ y = (x / 4 - y)；\n其他情况下，x ◎ y = 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: 5 □ 5 ◎ 8 + 1\n请将最终答案填入\\boxed{}中。"
},
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"simplified_expr": "((( ((( ((5 / 8)) * 4 + ((8 * 5)) * 1))) * 4 + 5 * 1)) + 1)",
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],
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} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y - y + x - 4.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - x + x * y.
and △, the rules are as follows:
on the real number field, 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: 3 △ 7 ♢ 2 ⊙ 1 / 10
Please fill your final answer in \boxed{}. | {
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"○": null,
"◎": null,
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"conditions": [],
"default_operation": " y - y + x - 4",
"precedence": 2
}
},
"target": null,
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"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = y - y + x - 4.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = y - x + x * y.\nand △, the rules are as follows:\non the real number field, 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: 3 △ 7 ♢ 2 ⊙ 1 / 10\nPlease fill your final answer in \\boxed{}."
},
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"seed": 18782456,
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} |
logic-v2 | Define ◇, the rules are as follows:
when y is even, x ◇ y = x * y + x ** y;
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: 3 ◇ 8 * 2 - 6
Please 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 = abs(x * y) + y.
and ⊗, the rules are as follows:
on the real number field, 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: 10 ◎ 2
Please fill your final answer in \boxed{}. | {
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},
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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 + 4 * x * 2.
and ○, the rules are as follows:
when x is a multiple of 5, x ○ y = y * y ** x + y;
otherwise, x ○ y = abs(x - y) + x * y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y + 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: 5 ⊙ 8 ▽ 8 ○ 6
Please fill your final answer in \boxed{}. | {
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},
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "x是5的倍数",
"operation": " y * y ** x + y"
}
],
"default_operation": " abs(x - y) + x * y",
"precedence": 3
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"question": "Define ⊙, the rules are as follows:\non the real number field, x ⊙ y = y / x + 4 * x * 2.\nand ○, the rules are as follows:\nwhen x is a multiple of 5, x ○ y = y * y ** x + y;\notherwise, x ○ y = abs(x - y) + x * y.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = y + 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: 5 ⊙ 8 ▽ 8 ○ 6\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( abs((( (( 8 + 8 - 8 / 8 + 8)) / 5 + 4 * 5 * 2)) - 6) + (( (( 8 + 8 - 8 / 8 + 8)) / 5 + 4 * 5 * 2)) * 6)",
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"precedence": 3
},
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"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x - x / y + y",
"precedence": 4
},
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "x是5的倍数",
"operation": " y * y ** x + y"
}
],
"default_operation": " abs(x - y) + x * y",
"precedence": 3
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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},
"seed": 1723836,
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} |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = x * 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: 9 % 9 △ 3
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 even, x △ y = x - y - 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: 8 △ 3
Please fill your final answer in \boxed{}. | {
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},
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"○": null,
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logic-v2 | 定义 ♡，规则如下：
当x是奇数时，x ♡ y = y - 3 + x + 4；
其他情况下，x ♡ y = (x + y - 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 % 1 ♡ 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大于y时，x △ y = x + y + x * x；
其他情况下，x △ y = y + y - x。
和 ♢，规则如下：
实数域上，x ♢ y = abs(x * y) - x + 1。
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 △ 7 ♢ 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 = (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: 4 ○ 8
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 + 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: 4 ○ 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 = y * 1 + x - y.
and ⊗, the rules are as follows:
when x is a multiple of 3, x ⊗ y = y + y + y + x;
otherwise, 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 ☆ 10 ⊗ 1 ⊗ 10
Please fill your final answer in \boxed{}. | {
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " y * 1 + x - y",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "2a40a813-7ee3-4dd3-a709-59a9c82fb55f"
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = y * 1 + x - y.\nand ⊗, the rules are as follows:\nwhen x is a multiple of 3, x ⊗ y = y + y + y + x;\notherwise, 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 ☆ 10 ⊗ 1 ⊗ 10\nPlease fill your final answer in \\boxed{}."
},
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"solutions_count": null,
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"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " y * 1 + x - y",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "2a40a813-7ee3-4dd3-a709-59a9c82fb55f"
},
"seed": 53323859,
"task_id": 253323859,
"task_type": "operation"
} |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = y + 3 + y * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x - y * y / x.
and ○, the rules are as follows:
when x is equal to y, x ○ y = x ⊙ y - x;
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: 5 ⊙ 2 % 4 ⊗ 2 ○ 6
Please fill your final answer in \boxed{}. | {
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"△": null,
"▽": null,
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"○": {
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"operation": " x ⊙ y - x"
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"♡": null,
"♢": null
},
"target": null,
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"trace_id": "84b37366-2450-42c8-bad9-7a22c4768848"
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"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = y + 3 + y * x.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = x - y * y / x.\nand ○, the rules are as follows:\nwhen x is equal to y, x ○ y = x ⊙ y - x;\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: 5 ⊙ 2 % 4 ⊗ 2 ○ 6\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( 6 / (( 2 + 3 + 2 * (( 5 - ((2 % 4)) * ((2 % 4)) / 5)))) + (( 2 + 3 + 2 * (( 5 - ((2 % 4)) * ((2 % 4)) / 5)))) + 6)",
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"conditions": [],
"default_operation": " x - y * y / x",
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},
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"△": null,
"▽": null,
"◇": null,
"○": {
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],
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},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"seed": 1441248,
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} |
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: 3 ▽ 5 ▽ 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 * 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: 3 ▽ 5 ▽ 10\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "3 ▽ 5 ▽ 10",
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"seed": 63104168,
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} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x + x - x * x / y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y ♢ x + y - x * x.
and ◇, the rules are as follows:
on the real number field, 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: 4 ◇ 10 ▽ 10
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-5897.701299",
"difficulty": 1,
"gpt_response": "",
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"△": null,
"▽": {
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"conditions": [],
"default_operation": " y ♢ x + y - x * x",
"precedence": 2
},
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y + x + x ♢ x",
"precedence": 4
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " x + x - x * x / y",
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}
},
"target": null,
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"trace_id": "cdf5579a-e7ae-4000-a2fa-e6363bf8a730"
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"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = x + x - x * x / y.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = y ♢ x + y - x * x.\nand ◇, the rules are as follows:\non the real number field, 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: 4 ◇ 10 ▽ 10\nPlease fill your final answer in \\boxed{}."
},
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"conditions": [],
"default_operation": " y ♢ x + y - x * x",
"precedence": 2
},
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y + x + x ♢ x",
"precedence": 4
},
"○": null,
"◎": null,
"☆": null,
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"♢": {
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"seed": 9575089,
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} |
logic-v2 | Define ♡, the rules are as follows:
when y is a multiple of 5, x ♡ y = y * y + x - y - y;
otherwise, x ♡ y = 5 + x * 3 * y - y.
and ♢, the rules are as follows:
when y is even, x ♢ y = x - y - x ♡ y - x;
otherwise, x ♢ y = 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: 1 ♡ 4
Please fill your final answer in \boxed{}. | {
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"◎": null,
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"operation": " y * y + x - y - y"
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"precedence": 5
},
"♢": {
"associativity": "left",
"conditions": [
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"operation": " x - y - x ♡ y - x"
}
],
"default_operation": " y ** x ♡ y + x + x",
"precedence": 3
}
},
"target": null,
"total_length": null,
"trace_id": "3fa04b24-fbab-40a6-8830-945e651675e4"
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"question": "Define ♡, the rules are as follows:\nwhen y is a multiple of 5, x ♡ y = y * y + x - y - y;\notherwise, x ♡ y = 5 + x * 3 * y - y.\nand ♢, the rules are as follows:\nwhen y is even, x ♢ y = x - y - x ♡ y - x;\notherwise, x ♢ y = 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: 1 ♡ 4\nPlease fill your final answer in \\boxed{}."
},
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"expression": "1 ♡ 4",
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"seed": 8675964,
"simplified_expr": "( 5 + 1 * 3 * 4 - 4)",
"solutions_count": null,
"symbol_definitions": {
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " y * y + x - y - y"
}
],
"default_operation": " 5 + x * 3 * y - y",
"precedence": 5
},
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "y是偶数",
"operation": " x - y - x ♡ y - x"
}
],
"default_operation": " y ** x ♡ y + x + x",
"precedence": 3
}
},
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"trace_id": "3fa04b24-fbab-40a6-8830-945e651675e4"
},
"seed": 8675964,
"task_id": 208675964,
"task_type": "operation"
} |
logic-v2 | Define ▽, 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: 4 ▽ 7 / 3
Please fill your final answer in \boxed{}. | {
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"default_operation": " (y - x + y ** x)",
"precedence": 1
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "c7ca858c-e78e-4af7-bf62-ead0cbfd125b"
},
"question": "Define ▽, 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: 4 ▽ 7 / 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "4 ▽ 7 / 3",
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"default_operation": " (y - x + y ** x)",
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"◇": null,
"○": null,
"◎": null,
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"seed": 62207009,
"task_id": 262207009,
"task_type": "operation"
} |
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 = x * y * y.
and ▽, the rules are as follows:
when x is even, x ▽ y = y + x ⊕ x;
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: 2 ⊕ 4 % 1 ☆ 2 ▽ 9
Please fill your final answer in \boxed{}. | {
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"answer": "50",
"difficulty": 1,
"gpt_response": "",
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"simplified_expr": "( (((( 4 - 2 / 4)) % 1)) * (((9 + (( 2 - 2 / 2))))) * (((9 + (( 2 - 2 / 2))))))",
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"△": null,
"▽": {
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"conditions": [
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"condition": "x是偶数",
"operation": " y + x ⊕ x"
}
],
"default_operation": " y - y / x",
"precedence": 3
},
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y * y",
"precedence": 2
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "da75c6b4-7b17-4712-8fb3-6d9a8597251c"
},
"question": "Define ⊕, 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 = x * y * y.\nand ▽, the rules are as follows:\nwhen x is even, x ▽ y = y + x ⊕ x;\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: 2 ⊕ 4 % 1 ☆ 2 ▽ 9\nPlease fill your final answer in \\boxed{}."
},
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"expression": "2 ⊕ 4 % 1 ☆ 2 ▽ 9",
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"seed": 4804101,
"simplified_expr": "( (((( 4 - 2 / 4)) % 1)) * (((9 + (( 2 - 2 / 2))))) * (((9 + (( 2 - 2 / 2))))))",
"solutions_count": null,
"symbol_definitions": {
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"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
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"condition": "x是偶数",
"operation": " y + x ⊕ x"
}
],
"default_operation": " y - y / x",
"precedence": 3
},
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y * y",
"precedence": 2
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "da75c6b4-7b17-4712-8fb3-6d9a8597251c"
},
"seed": 4804101,
"task_id": 204804101,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
when x is equal to y, x ◇ y = x + y / x;
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: 4
Please fill your final answer in \boxed{}. | {
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"answer": "4",
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"gpt_response": "",
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"◇": {
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"conditions": [
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"default_operation": " x / y - x",
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"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "c28298ae-1afd-4dcb-8f6e-cddc1bce7140"
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"question": "Define ◇, the rules are as follows:\nwhen x is equal to y, x ◇ y = x + y / x;\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: 4\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
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"num_of_numbers": null,
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"operators": null,
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"seed": 60779172,
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"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " x + y / x"
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],
"default_operation": " x / y - x",
"precedence": 3
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "c28298ae-1afd-4dcb-8f6e-cddc1bce7140"
},
"seed": 60779172,
"task_id": 260779172,
"task_type": "operation"
} |
logic-v2 | Define ○, the rules are as follows:
when x and y are both odd, x ○ y = x + x + 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: 8
Please fill your final answer in \boxed{}. | {
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"answer": "8",
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
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"conditions": [
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"operation": " x + x + x - y + y"
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],
"default_operation": " y ** x * y",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "60d62b2c-6299-4c37-8301-68071a348a39"
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"question": "Define ○, the rules are as follows:\nwhen x and y are both odd, x ○ y = x + x + x - y + y;\notherwise, 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: 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"n_types": null,
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"operators": null,
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"seed": 24134641,
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " x + x + x - y + y"
}
],
"default_operation": " y ** x * y",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "60d62b2c-6299-4c37-8301-68071a348a39"
},
"seed": 24134641,
"task_id": 224134641,
"task_type": "operation"
} |
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 - y - y + x + y。
和 ♡，规则如下：
实数域上，x ♡ y = 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: 5 ♡ 2 ○ 1 ⊙ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "142",
"difficulty": 1,
"gpt_response": "",
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"expression": "5 ♡ 2 ○ 1 ⊙ 3",
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"△": null,
"▽": null,
"◇": null,
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"conditions": [],
"default_operation": " x - y - y + x + y",
"precedence": 3
},
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y * x * x ⊙ y",
"precedence": 3
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "13ed541c-03df-4d44-b144-1345fe1186c7"
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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 - y - y + x + y。\n和 ♡，规则如下：\n实数域上，x ♡ y = 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: 5 ♡ 2 ○ 1 ⊙ 3\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "5 ♡ 2 ○ 1 ⊙ 3",
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"simplified_expr": "( 3 + (( (((((2 * 5)) * (( 2 + 5))))) - 1 - 1 + (((((2 * 5)) * (( 2 + 5))))) + 1)))",
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},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y - y + x + y",
"precedence": 3
},
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y * x * x ⊙ y",
"precedence": 3
},
"♢": null
},
"target": null,
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"trace_id": "13ed541c-03df-4d44-b144-1345fe1186c7"
},
"seed": 15711365,
"task_id": 215711365,
"task_type": "operation"
} |
logic-v2 | Define ⊕, the rules are as follows:
when x is a multiple of 3, x ⊕ y = y + y * y + x - 5;
otherwise, x ⊕ y = x - y * y / y + x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = (x) * y + x - y.
and □, the rules are as follows:
on the real number field, x □ y = y * y - 2 + 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 ** 3 ♢ 9 ⊕ 2 □ 2
Please fill your final answer in \boxed{}. | {
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"answer": "2166",
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"gpt_response": "",
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"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y - 2 + x",
"precedence": 3
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " (x) * y + x - y",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "b3c576d8-fdd6-4753-8110-8e0a5a895c1e"
},
"question": "Define ⊕, the rules are as follows:\nwhen x is a multiple of 3, x ⊕ y = y + y * y + x - 5;\notherwise, x ⊕ y = x - y * y / y + x.\nand ♢, the rules are as follows:\non the real number field, x ♢ y = (x) * y + x - y.\nand □, the rules are as follows:\non the real number field, x □ y = y * y - 2 + 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 ** 3 ♢ 9 ⊕ 2 □ 2\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "6 ** 3 ♢ 9 ⊕ 2 □ 2",
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"numbers": null,
"operators": null,
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"seed": 78406270,
"simplified_expr": "( (( 2 * 2 - 2 + 2)) + (( 2 * 2 - 2 + 2)) * (( 2 * 2 - 2 + 2)) + (( (((6 ** 3))) * 9 + ((6 ** 3)) - 9)) - 5)",
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],
"default_operation": " x - y * y / y + x",
"precedence": 1
},
"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y - 2 + x",
"precedence": 3
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " (x) * y + x - y",
"precedence": 1
}
},
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"trace_id": "b3c576d8-fdd6-4753-8110-8e0a5a895c1e"
},
"seed": 78406270,
"task_id": 278406270,
"task_type": "operation"
} |
logic-v2 | 定义 ▽，规则如下：
当x和y都是偶数时，x ▽ y = x * y；
其他情况下，x ▽ 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 ▽ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
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"default_operation": " x - y * 4",
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"◇": null,
"○": null,
"◎": null,
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"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "8a364598-34dc-4e3e-b44f-ed41c2df31cf"
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"question": "定义 ▽，规则如下：\n当x和y都是偶数时，x ▽ y = x * y；\n其他情况下，x ▽ 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 ▽ 1\n请将最终答案填入\\boxed{}中。"
},
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"○": null,
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},
"seed": 11887535,
"task_id": 211887535,
"task_type": "operation"
} |
logic-v2 | Define ☆, the rules are as follows:
when x is less than y, x ☆ y = y + x;
otherwise, x ☆ y = y - x - 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: 6 ☆ 3
Please fill your final answer in \boxed{}. | {
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"operation": " y + x"
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],
"default_operation": " y - x - x",
"precedence": 1
},
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y ☆ y",
"precedence": 4
},
"♢": null
},
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"question": "Define ☆, the rules are as follows:\nwhen x is less than y, x ☆ y = y + x;\notherwise, x ☆ y = y - x - 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: 6 ☆ 3\nPlease fill your final answer in \\boxed{}."
},
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"expression": "6 ☆ 3",
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"simplified_expr": "( 3 - 6 - 6)",
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"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
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"condition": "x小于y",
"operation": " y + x"
}
],
"default_operation": " y - x - x",
"precedence": 1
},
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y ☆ y",
"precedence": 4
},
"♢": null
},
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},
"seed": 53962951,
"task_id": 253962951,
"task_type": "operation"
} |
logic-v2 | Define ○, the rules are as follows:
when x is a multiple of 3, x ○ y = 2 + x + x * x * y;
otherwise, x ○ y = y / abs(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: 1
Please fill your final answer in \boxed{}. | {
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"expression": "1",
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"♢": null
},
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"trace_id": "1f4f58ec-2006-47a4-811b-d4940c317366"
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"question": "Define ○, the rules are as follows:\nwhen x is a multiple of 3, x ○ y = 2 + x + x * x * y;\notherwise, x ○ y = y / abs(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: 1\nPlease fill your final answer in \\boxed{}."
},
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"expression": "1",
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"seed": 27864823,
"simplified_expr": "1",
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"⊗": null,
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " 2 + x + x * x * y"
}
],
"default_operation": " y / abs(x * x / x)",
"precedence": 2
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "1f4f58ec-2006-47a4-811b-d4940c317366"
},
"seed": 27864823,
"task_id": 227864823,
"task_type": "operation"
} |
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 is less than y, x ♡ y = (y - 5 ☆ x) + x;
otherwise, x ♡ y = 2 / y * 1 - 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 ☆ 8 ** 2 ♡ 2
Please fill your final answer in \boxed{}. | {
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"expression": "1 ☆ 8 ** 2 ♡ 2",
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"♡": {
"associativity": "left",
"conditions": [
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"condition": "x小于y",
"operation": " (y - 5 ☆ x) + x"
}
],
"default_operation": " 2 / y * 1 - x",
"precedence": 1
},
"♢": null
},
"target": null,
"total_length": null,
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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 is less than y, x ♡ y = (y - 5 ☆ x) + x;\notherwise, x ♡ y = 2 / y * 1 - 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 ☆ 8 ** 2 ♡ 2\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "1 ☆ 8 ** 2 ♡ 2",
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"numbers": null,
"operators": null,
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"seed": 13725111,
"simplified_expr": "( 2 / 2 * 1 - (( ((8 ** 2)) ** 1 + 1)))",
"solutions_count": null,
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"▽": null,
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"○": null,
"◎": null,
"☆": {
"associativity": "left",
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"default_operation": " y ** x + x",
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},
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " (y - 5 ☆ x) + x"
}
],
"default_operation": " 2 / y * 1 - x",
"precedence": 1
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "4cadc07b-3a30-4073-b70b-e1eddfc17164"
},
"seed": 13725111,
"task_id": 213725111,
"task_type": "operation"
} |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * x / x - x / y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y / x ⊕ y + x.
and ○, the rules are as follows:
on the real number field, x ○ y = abs(x + 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: 7 ▽ 9 ⊕ 4 ○ 6
Please fill your final answer in \boxed{}. | {
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"difficulty": 1,
"gpt_response": "",
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"expression": "7 ▽ 9 ⊕ 4 ○ 6",
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"solutions_count": null,
"symbol_definitions": {
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"default_operation": " x * x / x - x / y",
"precedence": 2
},
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x ⊕ y + x",
"precedence": 3
},
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " abs(x + x) * x * y",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "ac9e22c1-9629-4cd7-9fd4-6274ddcf55ae"
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"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = x * x / x - x / y.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = y / x ⊕ y + x.\nand ○, the rules are as follows:\non the real number field, x ○ y = abs(x + 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: 7 ▽ 9 ⊕ 4 ○ 6\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "7 ▽ 9 ⊕ 4 ○ 6",
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"seed": 55332569,
"simplified_expr": "( ((((( ((9 / 7)) * ((9 / 7)) / ((9 / 7)) - ((9 / 7)) / 9)) + 7))) * ((((( ((9 / 7)) * ((9 / 7)) / ((9 / 7)) - ((9 / 7)) / 9)) + 7))) / ((((( ((9 / 7)) * ((9 / 7)) / ((9 / 7)) - ((9 / 7)) / 9)) + 7))) - ((((( ((9 / 7)) * ((9 / 7)) / ((9 / 7)) - ((9 / 7)) / 9)) + 7))) / (( abs(4 + 4) * 4 * 6)))",
"solutions_count": null,
"symbol_definitions": {
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"conditions": [],
"default_operation": " x * x / x - x / y",
"precedence": 2
},
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x ⊕ y + x",
"precedence": 3
},
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " abs(x + x) * x * y",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "ac9e22c1-9629-4cd7-9fd4-6274ddcf55ae"
},
"seed": 55332569,
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"task_type": "operation"
} |
logic-v2 | 定义 ♢，规则如下：
当x等于y时，x ♢ y = x - x - x - y；
其他情况下，x ♢ y = x + y * y - y + y。
和 ○，规则如下：
当x和y的和是奇数时，x ○ y = y - x - y ♢ y + y；
其他情况下，x ○ y = 1 * 2 + 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: 2 ○ 3 ♢ 10
请将最终答案填入\boxed{}中。 | {
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"condition": "x和y的和是奇数",
"operation": " y - x - y ♢ y + y"
}
],
"default_operation": " 1 * 2 + y / x",
"precedence": 4
},
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " x - x - x - y"
}
],
"default_operation": " x + y * y - y + y",
"precedence": 1
}
},
"target": null,
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"question": "定义 ♢，规则如下：\n当x等于y时，x ♢ y = x - x - x - y；\n其他情况下，x ♢ y = x + y * y - y + y。\n和 ○，规则如下：\n当x和y的和是奇数时，x ○ y = y - x - y ♢ y + y；\n其他情况下，x ○ y = 1 * 2 + 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: 2 ○ 3 ♢ 10\n请将最终答案填入\\boxed{}中。"
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],
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},
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
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}
],
"default_operation": " x + y * y - y + y",
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},
"seed": 899152,
"task_id": 200899152,
"task_type": "operation"
} |
logic-v2 | 定义 □，规则如下：
当x大于y时，x □ y = y * x - 4 + 4 / x；
其他情况下，x □ y = y * y + x + x。
和 ⊙，规则如下：
实数域上，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: 2 ⊙ 1 / 6 □ 8 □ 10
请将最终答案填入\boxed{}中。 | {
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"gpt_response": "",
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"seed": 47449379,
"simplified_expr": "( 10 * 10 + (( 8 * 8 + ((((((( 3 * 3 + 1 + 1)) - 2))) / 6)) + ((((((( 3 * 3 + 1 + 1)) - 2))) / 6)))) + (( 8 * 8 + ((((((( 3 * 3 + 1 + 1)) - 2))) / 6)) + ((((((( 3 * 3 + 1 + 1)) - 2))) / 6)))))",
"solutions_count": null,
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"condition": "x大于y",
"operation": " y * x - 4 + 4 / x"
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],
"default_operation": " y * y + x + x",
"precedence": 2
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"question": "定义 □，规则如下：\n当x大于y时，x □ y = y * x - 4 + 4 / x；\n其他情况下，x □ y = y * y + x + x。\n和 ⊙，规则如下：\n实数域上，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: 2 ⊙ 1 / 6 □ 8 □ 10\n请将最终答案填入\\boxed{}中。"
},
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"simplified_expr": "( 10 * 10 + (( 8 * 8 + ((((((( 3 * 3 + 1 + 1)) - 2))) / 6)) + ((((((( 3 * 3 + 1 + 1)) - 2))) / 6)))) + (( 8 * 8 + ((((((( 3 * 3 + 1 + 1)) - 2))) / 6)) + ((((((( 3 * 3 + 1 + 1)) - 2))) / 6)))))",
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logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y * x / y + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y - 2 - y * x.
and ◎, the rules are as follows:
when y is a multiple of 3, x ◎ y = x ♡ x + y + x;
otherwise, x ◎ y = 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: 3 ◎ 5 ⊗ 7 ♡ 7
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "( 7 * (( 7 - 2 - 7 * (( 3 - 3 + 5 * 5)))) / 7 + (( 7 - 2 - 7 * (( 3 - 3 + 5 * 5)))))",
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"operation": " x ♡ x + y + x"
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"precedence": 5
},
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y * x / y + x",
"precedence": 2
},
"♢": null
},
"target": null,
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"question": "Define ♡, the rules are as follows:\non the real number field, x ♡ y = y * x / y + x.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = y - 2 - y * x.\nand ◎, the rules are as follows:\nwhen y is a multiple of 3, x ◎ y = x ♡ x + y + x;\notherwise, x ◎ y = 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: 3 ◎ 5 ⊗ 7 ♡ 7\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( 7 * (( 7 - 2 - 7 * (( 3 - 3 + 5 * 5)))) / 7 + (( 7 - 2 - 7 * (( 3 - 3 + 5 * 5)))))",
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"operation": " x ♡ x + y + x"
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],
"default_operation": " x - x + y * y",
"precedence": 5
},
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y * x / y + x",
"precedence": 2
},
"♢": null
},
"target": null,
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},
"seed": 50597077,
"task_id": 250597077,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, 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: 10 ▽ 9
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 * 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 ▽ 9\nPlease fill your final answer in \\boxed{}."
},
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"▽": {
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"default_operation": " y - x * x / y",
"precedence": 3
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"seed": 75387815,
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} |
logic-v2 | 定义 ◇，规则如下：
当y是偶数时，x ◇ y = x - y + (y + x) + x；
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 ◇ 9
请将最终答案填入\boxed{}中。 | {
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"simplified_expr": "( 3 * 9 + 3)",
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"question": "定义 ◇，规则如下：\n当y是偶数时，x ◇ y = x - y + (y + x) + x；\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 ◇ 9\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"operators": null,
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"seed": 64081340,
"simplified_expr": "( 3 * 9 + 3)",
"solutions_count": null,
"symbol_definitions": {
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"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
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"condition": "y是偶数",
"operation": " x - y + (y + x) + x"
}
],
"default_operation": " x * y + x",
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"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
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},
"seed": 64081340,
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"task_type": "operation"
} |
logic-v2 | 定义 ⊙，规则如下：
当y是5的倍数时，x ⊙ y = y / x + y + x - y；
其他情况下，x ⊙ y = x + y + x。
和 ♡，规则如下：
当y是5的倍数时，x ♡ y = x * y ⊙ x；
其他情况下，x ♡ y = x + y - y ⊙ y + x。
和 □，规则如下：
实数域上，x □ y = y - y + 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: 10 ♡ 5 □ 3
请将最终答案填入\boxed{}中。 | {
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"□": {
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"default_operation": " y - y + y + y + x",
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"△": null,
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"◇": null,
"○": null,
"◎": null,
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"♡": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " x * y ⊙ x"
}
],
"default_operation": " x + y - y ⊙ y + x",
"precedence": 3
},
"♢": null
},
"target": null,
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"question": "定义 ⊙，规则如下：\n当y是5的倍数时，x ⊙ y = y / x + y + x - y；\n其他情况下，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；\n其他情况下，x ♡ y = x + y - y ⊙ y + x。\n和 □，规则如下：\n实数域上，x □ y = y - y + 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: 10 ♡ 5 □ 3\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"solutions_count": null,
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"operation": " y / x + y + x - y"
}
],
"default_operation": " x + y + x",
"precedence": 5
},
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " y - y + y + y + x",
"precedence": 2
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " x * y ⊙ x"
}
],
"default_operation": " x + y - y ⊙ y + x",
"precedence": 3
},
"♢": null
},
"target": null,
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},
"seed": 60174675,
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"task_type": "operation"
} |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = 1 / y * 1 ** 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
Please fill your final answer in \boxed{}. | {
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"answer": "4",
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"▽": null,
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"question": "Define ○, the rules are as follows:\non the real number field, x ○ y = 1 / y * 1 ** 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\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " 1 / y * 1 ** x",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"task_type": "operation"
} |
logic-v2 | Define ○, 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: 9 ○ 9 - 1 - 2
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.\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 ○ 9 - 1 - 2\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "9 ○ 9 - 1 - 2",
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"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
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logic-v2 | 定义 □，规则如下：
实数域上，x □ y = 2 + abs(3 + y) * y * x。
和 ▽，规则如下：
实数域上，x ▽ y = (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: 1 / 3 □ 3 + 9 ▽ 3
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ○，规则如下：
当x小于y时，x ○ y = abs(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: 5 ○ 3
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 = x ** (x + x * x + y);
otherwise, x ⊗ y = x / 5 - y - x + x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 2 + 4 + y / x - 1.
and △, the rules are as follows:
on the real number field, x △ y = y ◇ y - 5 + 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 △ 3 ◇ 3
Please 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 / 3) * 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 ○ 3 - 10
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 + x。
和 ▽，规则如下：
实数域上，x ▽ y = y * x + x。
和 □，规则如下：
当x是偶数时，x □ y = x ▽ y - x / x；
其他情况下，x □ y = y - 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: 8 □ 2 / 8 ▽ 6 - 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 = x * x + y + x。\n和 ▽，规则如下：\n实数域上，x ▽ y = y * x + x。\n和 □，规则如下：\n当x是偶数时，x □ y = x ▽ y - x / x；\n其他情况下，x □ y = y - 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: 8 □ 2 / 8 ▽ 6 - 5 ⊙ 6\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.
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 * 9 ◇ 1
Please 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 - 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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},
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"○": null,
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},
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"trace_id": "a2cfd7b4-22cf-451a-8a94-8b250f4df6c5"
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"question": "Define ▽, 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: 7\nPlease fill your final answer in \\boxed{}."
},
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"trace_id": "a2cfd7b4-22cf-451a-8a94-8b250f4df6c5"
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"seed": 11419298,
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} |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x / y + 3。
和 ⊕，规则如下：
当y是奇数时，x ⊕ y = x * y - (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: 2 ⊕ 3
请将最终答案填入\boxed{}中。 | {
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},
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"trace_id": "b0efb22c-2cc2-4a89-bf0c-79df35e620fa"
},
"question": "定义 ◎，规则如下：\n实数域上，x ◎ y = x / y + 3。\n和 ⊕，规则如下：\n当y是奇数时，x ⊕ y = x * y - (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: 2 ⊕ 3\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 3",
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"num_of_numbers": null,
"num_symbols": 2,
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"operators": null,
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"seed": 85273138,
"simplified_expr": "( 2 * 3 - (3))",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
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"△": null,
"▽": null,
"◇": null,
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"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " x / y + 3",
"precedence": 4
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "b0efb22c-2cc2-4a89-bf0c-79df35e620fa"
},
"seed": 85273138,
"task_id": 285273138,
"task_type": "operation"
} |
logic-v2 | Define ⊙, the rules are as follows:
when x is greater than y, x ⊙ y = y + x - y - x + x;
otherwise, x ⊙ y = x + 1 - 2 + y * x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = y + 3 + 2 - y - x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = 2 ** 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: 3 ♢ 10 ⊙ 7 % 4 ⊕ 5
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "32",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"solutions_count": null,
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"⊙": {
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"conditions": [
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"condition": "x大于y",
"operation": " y + x - y - x + x"
}
],
"default_operation": " x + 1 - 2 + y * x",
"precedence": 5
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y + 3 + 2 - y - x",
"precedence": 5
}
},
"target": null,
"total_length": null,
"trace_id": "20c06b54-bfe3-49b9-badd-55b3d37b1e06"
},
"question": "Define ⊙, the rules are as follows:\nwhen x is greater than y, x ⊙ y = y + x - y - x + x;\notherwise, x ⊙ y = x + 1 - 2 + y * x.\nand ♢, the rules are as follows:\non the real number field, x ♢ y = y + 3 + 2 - y - x.\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = 2 ** 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: 3 ♢ 10 ⊙ 7 % 4 ⊕ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "3 ♢ 10 ⊙ 7 % 4 ⊕ 5",
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"seed": 67267675,
"simplified_expr": "((((2 ** 5)) + (( ((((((((((((((((10 + 3)) + 2)) - 10)) - 3)) + 1)) - 2)) + ((7 * ((((((((10 + 3)) + 2)) - 10)) - 3)))))) % 4)) + 3 + 2 - ((((((((((((((((10 + 3)) + 2)) - 10)) - 3)) + 1)) - 2)) + ((7 * ((((((((10 + 3)) + 2)) - 10)) - 3)))))) % 4)) - 5))))",
"solutions_count": null,
"symbol_definitions": {
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"default_operation": " 2 ** y + y ♢ x",
"precedence": 2
},
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " y + x - y - x + x"
}
],
"default_operation": " x + 1 - 2 + y * x",
"precedence": 5
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y + 3 + 2 - y - x",
"precedence": 5
}
},
"target": null,
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"trace_id": "20c06b54-bfe3-49b9-badd-55b3d37b1e06"
},
"seed": 67267675,
"task_id": 267267675,
"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
when x is even, x ◎ y = x / 4 - y;
otherwise, x ◎ y = x / y.
and ♡, the rules are as follows:
when x is less than y, 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 ♡ 8
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"symbol_definitions": {
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],
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"precedence": 3
},
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " (x * y / y)"
}
],
"default_operation": " y + (x + y)",
"precedence": 3
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "b85797bb-dd94-4e19-854b-c93ffab659bb"
},
"question": "Define ◎, the rules are as follows:\nwhen x is even, x ◎ y = x / 4 - y;\notherwise, x ◎ y = x / y.\nand ♡, the rules are as follows:\nwhen x is less than y, x ♡ y = (x * y / y);\notherwise, 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 ♡ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 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": 14669618,
"simplified_expr": "( 8 + (10 + 8))",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " x / 4 - y"
}
],
"default_operation": " x / y",
"precedence": 3
},
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " (x * y / y)"
}
],
"default_operation": " y + (x + y)",
"precedence": 3
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "b85797bb-dd94-4e19-854b-c93ffab659bb"
},
"seed": 14669618,
"task_id": 214669618,
"task_type": "operation"
} |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x + 1 * 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 ○ 5 / 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 5 / 4",
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"seed": 5729267,
"simplified_expr": "((( 4 + 1 * 4 + 5)) / 4)",
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"symbol_definitions": {
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"□": null,
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"○": {
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"default_operation": " x + 1 * x + y",
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"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "4b935340-55e7-44eb-a866-48e29365dcda"
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"question": "定义 ○，规则如下：\n实数域上，x ○ y = x + 1 * 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 ○ 5 / 4\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 5 / 4",
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"seed": 5729267,
"simplified_expr": "((( 4 + 1 * 4 + 5)) / 4)",
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"○": {
"associativity": "left",
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"default_operation": " x + 1 * x + y",
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"◎": null,
"☆": null,
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},
"seed": 5729267,
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} |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = (y) + y - x - x * y.
and ◎, the rules are as follows:
when x is a multiple of 5, x ◎ y = x + y;
otherwise, x ◎ y = x - (y) - x + y - x.
and ○, the rules are as follows:
when x is equal to y, x ○ y = x ◎ 2 - 3 - y - y;
otherwise, 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: 7 ◎ 7 ○ 5 ⊕ 7 * 10
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-2790",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"expression": "7 ◎ 7 ○ 5 ⊕ 7 * 10",
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "x等于y",
"operation": " x ◎ 2 - 3 - y - y"
}
],
"default_operation": " y + x ⊕ y + y",
"precedence": 2
},
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "x是5的倍数",
"operation": " x + y"
}
],
"default_operation": " x - (y) - x + y - x",
"precedence": 3
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "bf0bd0f6-df5e-4751-9ed8-5d067c954348"
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"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = (y) + y - x - x * y.\nand ◎, the rules are as follows:\nwhen x is a multiple of 5, x ◎ y = x + y;\notherwise, x ◎ y = x - (y) - x + y - x.\nand ○, the rules are as follows:\nwhen x is equal to y, x ○ y = x ◎ 2 - 3 - y - y;\notherwise, 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: 7 ◎ 7 ○ 5 ⊕ 7 * 10\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 7 ○ 5 ⊕ 7 * 10",
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"seed": 45619656,
"simplified_expr": "((((((((((((7 + 7)) - 5)) - ((5 * 7)))) + (( (((((((7 + 7)) - 5)) - ((5 * 7))))) + ((((((7 + 7)) - 5)) - ((5 * 7)))) - ((((((((7 - 7)) - 7)) + 7)) - 7)) - ((((((((7 - 7)) - 7)) + 7)) - 7)) * ((((((7 + 7)) - 5)) - ((5 * 7)))))))) + ((((((7 + 7)) - 5)) - ((5 * 7))))))) * 10)",
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"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "x等于y",
"operation": " x ◎ 2 - 3 - y - y"
}
],
"default_operation": " y + x ⊕ y + y",
"precedence": 2
},
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "x是5的倍数",
"operation": " x + y"
}
],
"default_operation": " x - (y) - x + y - x",
"precedence": 3
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "bf0bd0f6-df5e-4751-9ed8-5d067c954348"
},
"seed": 45619656,
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} |
logic-v2 | Define △, the rules are as follows:
when y is even, x △ y = y + abs(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: 5
Please fill your final answer in \boxed{}. | {
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},
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"operation": " y + abs(x / 4)"
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],
"default_operation": " x ** y - x + y",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
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logic-v2 | Define ♢, the rules are as follows:
when the sum of x and y is even, x ♢ y = (x * y + x);
otherwise, x ♢ y = x + abs(x - y).
and ◇, the rules are as follows:
when x is greater than y, x ◇ y = x ♢ y + y;
otherwise, x ◇ y = y + (x / y).
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: 10 ◇ 2 ♢ 3 ◎ 3
Please fill your final answer in \boxed{}. | {
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"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y ◇ x",
"precedence": 4
},
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是偶数",
"operation": " (x * y + x)"
}
],
"default_operation": " x + abs(x - y)",
"precedence": 2
}
},
"target": null,
"total_length": null,
"trace_id": "636b1cfa-2d5f-47bc-b2e8-cd727fd9fb2f"
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"question": "Define ♢, the rules are as follows:\nwhen the sum of x and y is even, x ♢ y = (x * y + x);\notherwise, x ♢ y = x + abs(x - y).\nand ◇, the rules are as follows:\nwhen x is greater than y, x ◇ y = x ♢ y + y;\notherwise, x ◇ y = y + (x / y).\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: 10 ◇ 2 ♢ 3 ◎ 3\nPlease fill your final answer in \\boxed{}."
},
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"operation": " x ♢ y + y"
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"○": null,
"◎": {
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"conditions": [],
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"precedence": 4
},
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
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"condition": "x和y的和是偶数",
"operation": " (x * y + x)"
}
],
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"precedence": 2
}
},
"target": null,
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"trace_id": "636b1cfa-2d5f-47bc-b2e8-cd727fd9fb2f"
},
"seed": 46552880,
"task_id": 246552880,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
when x and y are both odd, x ▽ y = x * y - y;
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: 2 ▽ 8 + 3
Please fill your final answer in \boxed{}. | {
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},
"metadata": {
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"seed": 39503961,
"simplified_expr": "((( 3 * 8 - 2)) + 3)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " x * y - y"
}
],
"default_operation": " 3 * y - x",
"precedence": 4
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "bb8fa235-bd99-4fa4-845b-a2bb73a52ed2"
},
"seed": 39503961,
"task_id": 239503961,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
when x is less than y, x ◇ y = x - y - y * y ** y;
otherwise, x ◇ y = x - 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 ◇ 1 + 2
Please fill your final answer in \boxed{}. | {
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"symbol_definitions": {
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"□": null,
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"default_operation": " x - x * x + y * x",
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"○": null,
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"♡": null,
"♢": null
},
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"trace_id": "0b8b861a-6474-41fc-9bee-ca1b1c86fc81"
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"question": "Define ◇, the rules are as follows:\nwhen x is less than y, x ◇ y = x - y - y * y ** y;\notherwise, x ◇ y = x - 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 ◇ 1 + 2\nPlease fill your final answer in \\boxed{}."
},
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"seed": 11259560,
"simplified_expr": "((( 7 - 7 * 7 + 1 * 7)) + 2)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
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],
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"○": null,
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"♡": null,
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"seed": 11259560,
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} |
logic-v2 | Define ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = x ** x * y / x;
otherwise, x ⊗ y = x - x + y * y.
and ▽, the rules are as follows:
when x and y are both odd, x ▽ y = x + y + y ⊗ x;
otherwise, x ▽ y = y - x + x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ 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: 5 ⊙ 3 ⊗ 6 ▽ 7
Please fill your final answer in \boxed{}. | {
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"⊙": {
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"conditions": [],
"default_operation": " y ⊗ x",
"precedence": 2
},
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
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"condition": "x和y都是奇数",
"operation": " x + y + y ⊗ x"
}
],
"default_operation": " y - x + x",
"precedence": 1
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "a3e9ec94-eba0-45ef-8edd-0ea75785b82b"
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"question": "Define ⊗, the rules are as follows:\nwhen x is greater than y, x ⊗ y = x ** x * y / x;\notherwise, x ⊗ y = x - x + y * y.\nand ▽, the rules are as follows:\nwhen x and y are both odd, x ▽ y = x + y + y ⊗ x;\notherwise, x ▽ y = y - x + x.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ 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: 5 ⊙ 3 ⊗ 6 ▽ 7\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( 7 - (( ((( 3 - 3 + 5 * 5))) ** ((( 3 - 3 + 5 * 5))) * 6 / ((( 3 - 3 + 5 * 5))))) + (( ((( 3 - 3 + 5 * 5))) ** ((( 3 - 3 + 5 * 5))) * 6 / ((( 3 - 3 + 5 * 5))))))",
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}
],
"default_operation": " x - x + y * y",
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},
"⊙": {
"associativity": "left",
"conditions": [],
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"precedence": 2
},
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " x + y + y ⊗ x"
}
],
"default_operation": " y - x + x",
"precedence": 1
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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},
"seed": 92100902,
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} |
logic-v2 | Define □, the rules are as follows:
when x is equal to y, x □ y = x - x ** x * y * x;
otherwise, x □ y = (y / y / y - x / y).
and ☆, the rules are as follows:
on the real number field, 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: 8 □ 7
Please fill your final answer in \boxed{}. | {
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"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y - y / x - x",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "3c905b3f-7266-4dbc-93be-38b479cf99ba"
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"question": "Define □, the rules are as follows:\nwhen x is equal to y, x □ y = x - x ** x * y * x;\notherwise, x □ y = (y / y / y - x / y).\nand ☆, the rules are as follows:\non the real number field, 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: 8 □ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "8 □ 7",
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"solutions_count": null,
"symbol_definitions": {
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"operation": " x - x ** x * y * x"
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],
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},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y - y / x - x",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "3c905b3f-7266-4dbc-93be-38b479cf99ba"
},
"seed": 26273687,
"task_id": 226273687,
"task_type": "operation"
} |
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: 9
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ○，规则如下：
当y是5的倍数时，x ○ y = x * x - 1 + y；
其他情况下，x ○ y = x + 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: 10 * 1 - 8 ○ 1
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 = 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: 7 ▽ 9
Please fill your final answer in \boxed{}. | {
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logic-v2 | Define ○, the rules are as follows:
when y is odd, x ○ y = 1 - y - y - x / x;
otherwise, x ○ y = y + x * x * 2 ** 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 ○ 6 - 9 / 5
Please fill your final answer in \boxed{}. | {
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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 = x * y。
和 ⊙，规则如下：
实数域上，x ⊙ y = y + x。
和 ○，规则如下：
实数域上，x ○ y = abs(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: 9 ○ 8 ♢ 8
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 = x * y。\n和 ⊙，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 = abs(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: 9 ○ 8 ♢ 8\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3的倍数时，x ◎ y = x + y；
其他情况下，x ◎ y = y / 2 + 3 - x。
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: 3 ◎ 9
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ⊙, the rules are as follows:
when x and y are both even, x ⊙ y = x + x + y;
otherwise, x ⊙ y = y * x - y.
and △, the rules are as follows:
on the real number field, x △ y = x ** y - 2.
and ▽, the rules are as follows:
when x is greater than y, x ▽ y = 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: 9 ▽ 1 ⊙ 6 △ 2
Please fill your final answer in \boxed{}. | {
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"question": "Define ⊙, the rules are as follows:\nwhen x and y are both even, x ⊙ y = x + x + y;\notherwise, x ⊙ y = y * x - y.\nand △, the rules are as follows:\non the real number field, x △ y = x ** y - 2.\nand ▽, the rules are as follows:\nwhen x is greater than y, x ▽ y = y + x + y;\notherwise, 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 ▽ 1 ⊙ 6 △ 2\nPlease fill your final answer in \\boxed{}."
},
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} |
logic-v2 | 定义 ◇，规则如下：
当x是5的倍数时，x ◇ y = x + y / x；
其他情况下，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
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5的倍数时，x ◇ y = x + y / x；\n其他情况下，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: 8\n请将最终答案填入\\boxed{}中。"
},
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"◇": {
"associativity": "left",
"conditions": [
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"operation": " x + y / x"
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"default_operation": " y - x ** x",
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"seed": 67331853,
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logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = 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: 8 ○ 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 = 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: 8 ○ 1\nPlease fill your final answer in \\boxed{}."
},
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"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " y ** (y) - x - y",
"precedence": 3
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"seed": 79811498,
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logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = 2 - 1 / x * 5 + 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
请将最终答案填入\boxed{}中。 | {
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"answer": "6",
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"gpt_response": "",
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"expression": "6",
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"♢": null
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"question": "定义 ◇，规则如下：\n实数域上，x ◇ y = 2 - 1 / x * 5 + 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\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "6",
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"seed": 22057335,
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"⊕": null,
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"△": null,
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"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " 2 - 1 / x * 5 + y",
"precedence": 1
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"seed": 22057335,
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logic-v2 | Define □, the rules are as follows:
when x is a multiple of 5, x □ y = y * 4 * x - x;
otherwise, x □ y = x / y + y + y.
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 □ 6 ◇ 1
Please fill your final answer in \boxed{}. | {
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"△": null,
"▽": null,
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},
"○": null,
"◎": null,
"☆": null,
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"♢": null
},
"target": null,
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"trace_id": "0cc4720d-a4c6-4679-aa69-7edef4f24b3d"
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"question": "Define □, the rules are as follows:\nwhen x is a multiple of 5, x □ y = y * 4 * x - x;\notherwise, x □ y = x / y + y + y.\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: 8 □ 6 ◇ 1\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "8 □ 6 ◇ 1",
"fill_length": null,
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"is_solvable": null,
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"n_types": null,
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"operators": null,
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"seed": 36975976,
"simplified_expr": "( (( 8 / 6 + 6 + 6)) * 1 - (( 8 / 6 + 6 + 6)))",
"solutions_count": null,
"symbol_definitions": {
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"□": {
"associativity": "left",
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"△": null,
"▽": null,
"◇": {
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"conditions": [],
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},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "0cc4720d-a4c6-4679-aa69-7edef4f24b3d"
},
"seed": 36975976,
"task_id": 236975976,
"task_type": "operation"
} |
logic-v2 | 定义 △，规则如下：
当x大于y时，x △ y = x + y；
其他情况下，x △ y = y * 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: 9 △ 10 △ 8 * 8
请将最终答案填入\boxed{}中。 | {
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"question": "定义 △，规则如下：\n当x大于y时，x △ y = x + y；\n其他情况下，x △ y = y * 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: 9 △ 10 △ 8 * 8\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"simplified_expr": "((( (( 10 * 10 + 10 * 9 - 9)) + 8)) * 8)",
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"△": {
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},
"seed": 80098550,
"task_id": 280098550,
"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x - y - 5 - x - y.
and ☆, the rules are as follows:
when x and y are both odd, x ☆ y = y + 5 ◎ 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: 8 ☆ 6 / 10 ◎ 5
Please fill your final answer in \boxed{}. | {
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"△": null,
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"○": null,
"◎": {
"associativity": "left",
"conditions": [],
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"precedence": 1
},
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " y + 5 ◎ x"
}
],
"default_operation": " x ◎ (y - x) * x + x",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
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},
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"expression": "8 ☆ 6 / 10 ◎ 5",
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"operators": null,
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"seed": 16219473,
"simplified_expr": "( ((((((( 8 - ((((6 - 8)) * 8)) - 5 - 8 - ((((6 - 8)) * 8)))) + 8))) / 10)) - 5 - 5 - ((((((( 8 - ((((6 - 8)) * 8)) - 5 - 8 - ((((6 - 8)) * 8)))) + 8))) / 10)) - 5)",
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"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y - 5 - x - y",
"precedence": 1
},
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " y + 5 ◎ x"
}
],
"default_operation": " x ◎ (y - x) * x + x",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "7d8a9639-3173-4a8f-b54b-7f8e74b3acad"
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"seed": 16219473,
"task_id": 216219473,
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logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = abs(y) ** x。
和 ▽，规则如下：
当x小于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: 3 / 4 ☆ 2 ▽ 4
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 * (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: 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 * (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: 9\n请将最终答案填入\\boxed{}中。"
},
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"○": {
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"default_operation": " y * x * (x)",
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},
"◎": null,
"☆": null,
"♡": null,
"♢": null
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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:
when y is odd, x ◎ y = x ☆ y - (1);
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: 5 % 10 ☆ 6 ◎ 5
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "5",
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"♡": 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:\nwhen y is odd, x ◎ y = x ☆ y - (1);\notherwise, 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: 5 % 10 ☆ 6 ◎ 5\nPlease fill your final answer in \\boxed{}."
},
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"seed": 49970462,
"simplified_expr": "(5 % ((((( ((10 + 6)) + 5)) - 1))))",
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},
"seed": 49970462,
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} |
logic-v2 | 定义 ⊕，规则如下：
当y是奇数时，x ⊕ y = abs(y + x)；
其他情况下，x ⊕ y = y ** abs(x / y - 5 / y)。
和 ♢，规则如下：
实数域上，x ♢ y = (x) ⊕ y + 5 - y - x。
和 ⊗，规则如下：
当x等于y时，x ⊗ y = y ♢ 1 - x；
其他情况下，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: 8 ♢ 5 ⊗ 9
请将最终答案填入\boxed{}中。 | {
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},
"⊗": {
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"conditions": [
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"condition": "x等于y",
"operation": " y ♢ 1 - x"
}
],
"default_operation": " y ♢ x",
"precedence": 4
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
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"default_operation": " (x) ⊕ y + 5 - y - x",
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}
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"question": "定义 ⊕，规则如下：\n当y是奇数时，x ⊕ y = abs(y + x)；\n其他情况下，x ⊕ y = y ** abs(x / y - 5 / y)。\n和 ♢，规则如下：\n实数域上，x ♢ y = (x) ⊕ y + 5 - y - x。\n和 ⊗，规则如下：\n当x等于y时，x ⊗ y = y ♢ 1 - x；\n其他情况下，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: 8 ♢ 5 ⊗ 9\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "8 ♢ 5 ⊗ 9",
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"seed": 36079078,
"simplified_expr": "(((((((( (((((((abs((5 + 9))) + 5)) - 5)) - 9)) ** abs(8 / (((((((abs((5 + 9))) + 5)) - 5)) - 9)) - 5 / (((((((abs((5 + 9))) + 5)) - 5)) - 9))))) + 5)) - (((((((abs((5 + 9))) + 5)) - 5)) - 9)))) - 8))",
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"⊗": {
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"operation": " y ♢ 1 - x"
}
],
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"△": null,
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"◇": null,
"○": null,
"◎": null,
"☆": null,
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"♢": {
"associativity": "left",
"conditions": [],
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"seed": 36079078,
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"task_type": "operation"
} |
logic-v2 | 定义 ○，规则如下：
当x和y的和是奇数时，x ○ y = abs(x - y) - y；
其他情况下，x ○ y = y - x + x。
和 ⊕，规则如下：
实数域上，x ⊕ y = x ○ y。
和 ♢，规则如下：
实数域上，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: 7 ○ 5 ♢ 10 ⊕ 5
请将最终答案填入\boxed{}中。 | {
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},
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"expression": "7 ○ 5 ♢ 10 ⊕ 5",
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"solutions_count": null,
"symbol_definitions": {
"⊕": {
"associativity": "left",
"conditions": [],
"default_operation": " x ○ y",
"precedence": 3
},
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "x和y的和是奇数",
"operation": " abs(x - y) - y"
}
],
"default_operation": " y - x + x",
"precedence": 2
},
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y ⊕ x",
"precedence": 2
}
},
"target": null,
"total_length": null,
"trace_id": "137d6386-865b-41ea-8d10-8ce3703c48d3"
},
"seed": 29792987,
"task_id": 229792987,
"task_type": "operation"
} |
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