env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y - x * 2 - 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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"expression": "5",
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"num_of_numbers": null,
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"numbers": null,
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"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": {
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"conditions": [],
"default_operation": " y - x * 2 - y",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": 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 = y - x * 2 - 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\nPlease fill your final answer in \\boxed{}."
},
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"closing_sequence": null,
"expression": "5",
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"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
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"seed": 69822369,
"simplified_expr": "5",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x * 2 - y",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"target": null,
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"trace_id": "cebd3c9b-d8ae-412f-9cc2-d3034ab69949"
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"seed": 69822369,
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logic-v2 | Define ⊗, the rules are as follows:
when x is less than y, x ⊗ y = x * x * abs(y);
otherwise, x ⊗ y = y - y + x * x.
and △, the rules are as follows:
on the real number field, x △ y = 4 * x + y * x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x ⊗ y + x + y.
The precedence of operations: ⊗ = △ > ** > * = / = % > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 △ 2 ⊗ 10
Please fill your final answer in \boxed{}. | {
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"expression": "3 △ 2 ⊗ 10",
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"numbers": null,
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"seed": 62476278,
"simplified_expr": "( 10 - 10 + (( 4 * 3 + 2 * 3)) * (( 4 * 3 + 2 * 3)))",
"solutions_count": null,
"symbol_definitions": {
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"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " 4 * x + y * x",
"precedence": 5
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " x ⊗ y + x + y",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "9f299fc6-eefc-429d-a865-bc8dfc6e5bb0"
},
"question": "Define ⊗, the rules are as follows:\nwhen x is less than y, x ⊗ y = x * x * abs(y);\notherwise, x ⊗ y = y - y + x * x.\nand △, the rules are as follows:\non the real number field, x △ y = 4 * x + y * x.\nand ♢, the rules are as follows:\non the real number field, x ♢ y = x ⊗ y + x + y.\nThe precedence of operations: ⊗ = △ > ** > * = / = % > + = - = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 △ 2 ⊗ 10\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "3 △ 2 ⊗ 10",
"fill_length": null,
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"is_solvable": null,
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"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 62476278,
"simplified_expr": "( 10 - 10 + (( 4 * 3 + 2 * 3)) * (( 4 * 3 + 2 * 3)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " x * x * abs(y)"
}
],
"default_operation": " y - y + x * x",
"precedence": 5
},
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " 4 * x + y * x",
"precedence": 5
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " x ⊗ y + x + y",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "9f299fc6-eefc-429d-a865-bc8dfc6e5bb0"
},
"seed": 62476278,
"task_id": 262476278,
"task_type": "operation"
} |
logic-v2 | Define △, the rules are as follows:
on the real number field, 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: 1 % 3 △ 8
Please fill your final answer in \boxed{}. | {
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"answer": "1",
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"gpt_response": "",
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"expression": "1 % 3 △ 8",
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 79319555,
"simplified_expr": "(1 % (( 3 * (3 + 8) / 8)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " x * (x + y) / y",
"precedence": 5
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "ac8bad18-457c-4997-bfbe-51459611298f"
},
"question": "Define △, the rules are as follows:\non the real number field, 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: 1 % 3 △ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "1 % 3 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
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"seed": 79319555,
"simplified_expr": "(1 % (( 3 * (3 + 8) / 8)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " x * (x + y) / y",
"precedence": 5
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "ac8bad18-457c-4997-bfbe-51459611298f"
},
"seed": 79319555,
"task_id": 279319555,
"task_type": "operation"
} |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y + y * x。
和 ▽，规则如下：
实数域上，x ▽ y = 2 / x / y + y。
和 ☆，规则如下：
当x等于y时，x ☆ y = 1 ▽ y * x；
其他情况下，x ☆ 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: 10 ▽ 9 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-8.911385",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 9 ☆ 2",
"fill_length": null,
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"n_types": null,
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"numbers": null,
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"seed": 44868453,
"simplified_expr": "(((((( 2 / ((((((2 / 10)) / 9)) + 9)) / 2 + 2)) - 2)) - ((((((2 / 10)) / 9)) + 9))))",
"solutions_count": null,
"symbol_definitions": {
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"□": null,
"△": null,
"▽": {
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"conditions": [],
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"precedence": 5
},
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " 1 ▽ y * x"
}
],
"default_operation": " x ▽ y - y - x",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "96b52770-8101-485b-835f-28c419a48d85"
},
"question": "定义 ⊗，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 = 2 / x / y + y。\n和 ☆，规则如下：\n当x等于y时，x ☆ y = 1 ▽ y * x；\n其他情况下，x ☆ 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: 10 ▽ 9 ☆ 2\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "10 ▽ 9 ☆ 2",
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"seed": 44868453,
"simplified_expr": "(((((( 2 / ((((((2 / 10)) / 9)) + 9)) / 2 + 2)) - 2)) - ((((((2 / 10)) / 9)) + 9))))",
"solutions_count": null,
"symbol_definitions": {
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},
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"□": null,
"△": null,
"▽": {
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"conditions": [],
"default_operation": " 2 / x / y + y",
"precedence": 5
},
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " 1 ▽ y * x"
}
],
"default_operation": " x ▽ y - y - x",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "96b52770-8101-485b-835f-28c419a48d85"
},
"seed": 44868453,
"task_id": 244868453,
"task_type": "operation"
} |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y - y - x - x。
和 ▽，规则如下：
实数域上，x ▽ y = y * y - 5 * y + x。
和 □，规则如下：
实数域上，x □ y = x * y △ y - 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 □ 6 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "72",
"difficulty": 1,
"gpt_response": "",
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"seed": 12252559,
"simplified_expr": "( 8 - 8 - ((((( 6 - 6 - ((1 * 6)) - ((1 * 6)))) - ((6 * 4))))) - ((((( 6 - 6 - ((1 * 6)) - ((1 * 6)))) - ((6 * 4))))))",
"solutions_count": null,
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},
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y - y - x - x",
"precedence": 2
},
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y - 5 * y + x",
"precedence": 3
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "e581f045-5f6c-4f76-8b03-114b60f2f428"
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"question": "定义 △，规则如下：\n实数域上，x △ y = y - y - x - x。\n和 ▽，规则如下：\n实数域上，x ▽ y = y * y - 5 * y + x。\n和 □，规则如下：\n实数域上，x □ y = x * y △ y - 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 □ 6 △ 8\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "1 □ 6 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"num_of_numbers": null,
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"numbers": null,
"operators": null,
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"seed": 12252559,
"simplified_expr": "( 8 - 8 - ((((( 6 - 6 - ((1 * 6)) - ((1 * 6)))) - ((6 * 4))))) - ((((( 6 - 6 - ((1 * 6)) - ((1 * 6)))) - ((6 * 4))))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y △ y - y * 4",
"precedence": 5
},
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y - y - x - x",
"precedence": 2
},
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y - 5 * y + x",
"precedence": 3
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "e581f045-5f6c-4f76-8b03-114b60f2f428"
},
"seed": 12252559,
"task_id": 212252559,
"task_type": "operation"
} |
logic-v2 | 定义 □，规则如下：
当y是5的倍数时，x □ y = x + y * x；
其他情况下，x □ y = y * x * y。
和 ◇，规则如下：
实数域上，x ◇ y = y - x - x。
运算优先级：□ = ◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 □ 8 ◇ 7
请将最终答案填入\boxed{}中。 | {
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"answer": "-761",
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"gpt_response": "",
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"expression": "6 □ 8 ◇ 7",
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"△": null,
"▽": null,
"◇": {
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},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"target": null,
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"question": "定义 □，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 = y * x * y。\n和 ◇，规则如下：\n实数域上，x ◇ y = y - x - x。\n运算优先级：□ = ◇ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 6 □ 8 ◇ 7\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "6 □ 8 ◇ 7",
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"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 81568761,
"simplified_expr": "( 7 - (( 8 * 6 * 8)) - (( 8 * 6 * 8)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " x + y * x"
}
],
"default_operation": " y * x * y",
"precedence": 5
},
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x - x",
"precedence": 5
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "f912d875-0c03-4fe9-9346-02c1c327f4ff"
},
"seed": 81568761,
"task_id": 281568761,
"task_type": "operation"
} |
logic-v2 | 定义 ⊕，规则如下：
当y是奇数时，x ⊕ y = y - y - y - x；
其他情况下，x ⊕ y = y + x - y + y。
和 ♡，规则如下：
当x和y都是偶数时，x ♡ y = y ** x；
其他情况下，x ♡ y = (y + x)。
和 ◇，规则如下：
当y是偶数时，x ◇ y = y + x；
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: 4 ◇ 6 ⊕ 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊕，规则如下：\n当y是奇数时，x ⊕ y = y - y - y - x；\n其他情况下，x ⊕ y = y + x - y + y。\n和 ♡，规则如下：\n当x和y都是偶数时，x ♡ y = y ** x；\n其他情况下，x ♡ y = (y + x)。\n和 ◇，规则如下：\n当y是偶数时，x ◇ y = y + x；\n其他情况下，x ◇ y = y - x ⊕ 3 * 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 ◇ 6 ⊕ 10\n请将最终答案填入\\boxed{}中。"
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logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * y * x - x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = 3 - x * y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x / 3 / 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: 4 ☆ 4 ⊕ 10 ▽ 3 + 5
Please fill your final answer in \boxed{}. | {
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"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = x * y * x - x.\nand ☆, the rules are as follows:\non the real number field, x ☆ y = 3 - x * y.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = x / 3 / 1 - 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 ☆ 4 ⊕ 10 ▽ 3 + 5\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 - 4 + y.
and ◎, the rules are as follows:
when y is a multiple of 5, x ◎ y = x ♢ y - y;
otherwise, x ◎ y = y + x - 2.
and ☆, the rules are as follows:
when y is a multiple of 5, x ☆ y = abs(y * x) * x;
otherwise, x ☆ y = x + y - 5.
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 ♢ 2 ☆ 8 ◎ 1
Please fill your final answer in \boxed{}. | {
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"☆": {
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"condition": "y是5的倍数",
"operation": " abs(y * x) * x"
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"default_operation": " x + y - 5",
"precedence": 5
},
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"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = x - 4 + y.\nand ◎, the rules are as follows:\nwhen y is a multiple of 5, x ◎ y = x ♢ y - y;\notherwise, x ◎ y = y + x - 2.\nand ☆, the rules are as follows:\nwhen y is a multiple of 5, x ☆ y = abs(y * x) * x;\notherwise, x ☆ y = x + y - 5.\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 ♢ 2 ☆ 8 ◎ 1\nPlease 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 - y - y - x.
and ⊕, the rules are as follows:
when y is even, x ⊕ y = (4 □ x + 3) * y - y;
otherwise, x ⊕ y = (2 + y * x).
The precedence of operations: □ > ** > * = / = % = ⊕ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 / 8 * 9 ⊕ 5 □ 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 + x - y - y - x.\nand ⊕, the rules are as follows:\nwhen y is even, x ⊕ y = (4 □ x + 3) * y - y;\notherwise, x ⊕ y = (2 + y * x).\nThe precedence of operations: □ > ** > * = / = % = ⊕ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 / 8 * 9 ⊕ 5 □ 8\nPlease fill your final answer in \\boxed{}."
},
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"precedence": 4
},
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
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},
"seed": 28639788,
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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: 4
Please fill your final answer in \boxed{}. | {
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},
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"expression": "4",
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"default_operation": " y * x + y",
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"♢": null
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} |
logic-v2 | Define ☆, the rules are as follows:
when x and y are both odd, x ☆ y = x - y * y;
otherwise, x ☆ y = x * y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * x * y.
The precedence of operations: ** > * = / = % = ☆ = ⊗ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ☆ 9 ⊗ 1
Please fill your final answer in \boxed{}. | {
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
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"condition": "x和y都是奇数",
"operation": " x - y * y"
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"default_operation": " x * y",
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"♡": null,
"♢": null
},
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},
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"simplified_expr": "( (( 3 - 9 * 9)) * (( 3 - 9 * 9)) * 1)",
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"operation": " x - y * y"
}
],
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"♢": null
},
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"seed": 80153539,
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} |
logic-v2 | Define △, 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: 7 / 10 △ 3 - 9
Please fill your final answer in \boxed{}. | {
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"difficulty": 1,
"gpt_response": "",
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"question": "Define △, 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: 7 / 10 △ 3 - 9\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "7 / 10 △ 3 - 9",
"fill_length": null,
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"n_types": null,
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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 = y / x / y + x + y.
and □, the rules are as follows:
on the real number field, x □ y = y - 5 + y / x + 2.
and ○, the rules are as follows:
on the real number field, x ○ y = 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: 3 + 2 ⊗ 6 ⊗ 8 ○ 7 □ 8
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "7.914284",
"difficulty": 1,
"gpt_response": "",
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"seed": 79382726,
"simplified_expr": "(3 + (( 8 - 5 + 8 / (((((7 + (( ((((((((8 / ((((((((6 / 2)) / 6)) + 2)) + 6)))) / 8)) + ((((((((6 / 2)) / 6)) + 2)) + 6)))) + 8)) - 5 + ((((((((8 / ((((((((6 / 2)) / 6)) + 2)) + 6)))) / 8)) + ((((((((6 / 2)) / 6)) + 2)) + 6)))) + 8)) / 7 + 2)))) - ((7 * ((((((((8 / ((((((((6 / 2)) / 6)) + 2)) + 6)))) / 8)) + ((((((((6 / 2)) / 6)) + 2)) + 6)))) + 8))))))) + 2)))",
"solutions_count": null,
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},
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"□": {
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"conditions": [],
"default_operation": " y - 5 + y / x + 2",
"precedence": 2
},
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " y + y □ x - y * x",
"precedence": 3
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "82056ca3-90ca-4646-b403-8212cd206b28"
},
"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = y / x / y + x + y.\nand □, the rules are as follows:\non the real number field, x □ y = y - 5 + y / x + 2.\nand ○, the rules are as follows:\non the real number field, x ○ y = 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: 3 + 2 ⊗ 6 ⊗ 8 ○ 7 □ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "3 + 2 ⊗ 6 ⊗ 8 ○ 7 □ 8",
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"simplified_expr": "(3 + (( 8 - 5 + 8 / (((((7 + (( ((((((((8 / ((((((((6 / 2)) / 6)) + 2)) + 6)))) / 8)) + ((((((((6 / 2)) / 6)) + 2)) + 6)))) + 8)) - 5 + ((((((((8 / ((((((((6 / 2)) / 6)) + 2)) + 6)))) / 8)) + ((((((((6 / 2)) / 6)) + 2)) + 6)))) + 8)) / 7 + 2)))) - ((7 * ((((((((8 / ((((((((6 / 2)) / 6)) + 2)) + 6)))) / 8)) + ((((((((6 / 2)) / 6)) + 2)) + 6)))) + 8))))))) + 2)))",
"solutions_count": null,
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},
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"□": {
"associativity": "left",
"conditions": [],
"default_operation": " y - 5 + y / x + 2",
"precedence": 2
},
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " y + y □ x - y * x",
"precedence": 3
},
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"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"seed": 79382726,
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} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y - x / (y - 3 - y).
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x / y / abs(x - x + x).
and ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = 4 / x + x * x ◎ y;
otherwise, x ⊙ y = 1 - y - x ⊕ x.
The precedence of operations: ** = ⊕ = ⊙ > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ◎ 3 ⊕ 9 ⊙ 1
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-5.666667",
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"solutions_count": null,
"symbol_definitions": {
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"conditions": [],
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"precedence": 3
},
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " 4 / x + x * x ◎ y"
}
],
"default_operation": " 1 - y - x ⊕ x",
"precedence": 3
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x / (y - 3 - y)",
"precedence": 2
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "be7883cd-fb84-44a0-9d90-befa772e8141"
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = y - x / (y - 3 - y).\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = x / y / abs(x - x + x).\nand ⊙, the rules are as follows:\nwhen x and y are both odd, x ⊙ y = 4 / x + x * x ◎ y;\notherwise, x ⊙ y = 1 - y - x ⊕ x.\nThe precedence of operations: ** = ⊕ = ⊙ > * = / = % = ◎ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 ◎ 3 ⊕ 9 ⊙ 1\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "10 ◎ 3 ⊕ 9 ⊙ 1",
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"n_types": null,
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"num_of_numbers": null,
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"seed": 91956851,
"simplified_expr": "( (((((1 - 1)) - (( ((((3 / 9)) / (abs((((3 - 3)) + 3))))) / ((((3 / 9)) / (abs((((3 - 3)) + 3))))) / abs(((((3 / 9)) / (abs((((3 - 3)) + 3))))) - ((((3 / 9)) / (abs((((3 - 3)) + 3))))) + ((((3 / 9)) / (abs((((3 - 3)) + 3))))))))))) - 10 / ((((((1 - 1)) - (( ((((3 / 9)) / (abs((((3 - 3)) + 3))))) / ((((3 / 9)) / (abs((((3 - 3)) + 3))))) / abs(((((3 / 9)) / (abs((((3 - 3)) + 3))))) - ((((3 / 9)) / (abs((((3 - 3)) + 3))))) + ((((3 / 9)) / (abs((((3 - 3)) + 3))))))))))) - 3 - (((((1 - 1)) - (( ((((3 / 9)) / (abs((((3 - 3)) + 3))))) / ((((3 / 9)) / (abs((((3 - 3)) + 3))))) / abs(((((3 / 9)) / (abs((((3 - 3)) + 3))))) - ((((3 / 9)) / (abs((((3 - 3)) + 3))))) + ((((3 / 9)) / (abs((((3 - 3)) + 3)))))))))))))",
"solutions_count": null,
"symbol_definitions": {
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"conditions": [],
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},
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " 4 / x + x * x ◎ y"
}
],
"default_operation": " 1 - y - x ⊕ x",
"precedence": 3
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
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"precedence": 2
},
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"♡": null,
"♢": null
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"seed": 91956851,
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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:
on the real number field, x ⊙ y = y * y - (x ⊕ 1).
and □, the rules are as follows:
when x is equal to y, x □ y = y + x + y / y;
otherwise, x □ y = y ⊕ y / x.
The precedence of operations: ** > * = / = % = ⊕ = ⊙ > + = - = □。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 □ 4 ⊕ 10 ⊙ 4
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "(((( ((((4 * 4)) - ((((4 + ((10 * 10)))) + ((1 * 1)))))) + ((((4 * 4)) - ((((4 + ((10 * 10)))) + ((1 * 1)))))) * ((((4 * 4)) - ((((4 + ((10 * 10)))) + ((1 * 1)))))))) / 2))",
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},
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"conditions": [
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"condition": "x等于y",
"operation": " y + x + y / y"
}
],
"default_operation": " y ⊕ y / x",
"precedence": 1
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "c9f663d9-6905-4dcf-9f21-455d856ee2d1"
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"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = x + y * y.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = y * y - (x ⊕ 1).\nand □, the rules are as follows:\nwhen x is equal to y, x □ y = y + x + y / y;\notherwise, x □ y = y ⊕ y / x.\nThe precedence of operations: ** > * = / = % = ⊕ = ⊙ > + = - = □。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 □ 4 ⊕ 10 ⊙ 4\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "(((( ((((4 * 4)) - ((((4 + ((10 * 10)))) + ((1 * 1)))))) + ((((4 * 4)) - ((((4 + ((10 * 10)))) + ((1 * 1)))))) * ((((4 * 4)) - ((((4 + ((10 * 10)))) + ((1 * 1)))))))) / 2))",
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"symbol_definitions": {
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"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y - (x ⊕ 1)",
"precedence": 2
},
"□": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " y + x + y / y"
}
],
"default_operation": " y ⊕ y / x",
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},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
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"trace_id": "c9f663d9-6905-4dcf-9f21-455d856ee2d1"
},
"seed": 1328439,
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} |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = (x * y).
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ○ 3
Please fill your final answer in \boxed{}. | {
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"answer": "12",
"difficulty": 1,
"gpt_response": "",
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"expression": "4 ○ 3",
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"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
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"○": {
"associativity": "left",
"conditions": [],
"default_operation": " (x * y)",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "66532923-cfe5-4ba8-b27e-600b1e821ef8"
},
"question": "Define ○, the rules are as follows:\non the real number field, x ○ y = (x * y).\nThe precedence of operations: ○ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ○ 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"fill_length": null,
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"language": "english",
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"simplified_expr": "( (4 * 3))",
"solutions_count": null,
"symbol_definitions": {
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " (x * y)",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "66532923-cfe5-4ba8-b27e-600b1e821ef8"
},
"seed": 77106674,
"task_id": 277106674,
"task_type": "operation"
} |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y + y - x / x。
和 ◎，规则如下：
实数域上，x ◎ y = x + y + x * y。
和 ▽，规则如下：
当x是3的倍数时，x ▽ y = x / x * y * y + x；
其他情况下，x ▽ y = 1 * y ◎ x + 2。
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 ◎ 5 ⊙ 4 ▽ 4 ⊙ 3
请将最终答案填入\boxed{}中。 | {
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"expression": "6 ◎ 5 ⊙ 4 ▽ 4 ⊙ 3",
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"question": "定义 ⊙，规则如下：\n实数域上，x ⊙ y = y + y - x / x。\n和 ◎，规则如下：\n实数域上，x ◎ y = x + y + x * y。\n和 ▽，规则如下：\n当x是3的倍数时，x ▽ y = x / x * y * y + x；\n其他情况下，x ▽ y = 1 * y ◎ x + 2。\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 ◎ 5 ⊙ 4 ▽ 4 ⊙ 3\n请将最终答案填入\\boxed{}中。"
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logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = (x + 3 - y) - y。
和 □，规则如下：
实数域上，x □ y = y - x - x。
和 ⊗，规则如下：
当y是偶数时，x ⊗ y = x / abs(y ** y) * x；
其他情况下，x ⊗ y = x + y - y。
运算优先级：** = ⊗ > * = / = % > + = - = ○ = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 * 7 ⊗ 10 ○ 5 □ 4
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | Define ⊕, the rules are as follows:
when x is odd, x ⊕ y = x - y - y - x - x;
otherwise, x ⊕ y = x / y * x + x - 1.
and ○, the rules are as follows:
when x is even, x ○ y = 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: 9 ⊕ 5 + 5 ○ 1
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 = 4 / (x) - y。
和 ◇，规则如下：
实数域上，x ◇ y = x + 5 □ 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: 3 % 1 ◇ 10 □ 2
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 = 4 / (x) - y。\n和 ◇，规则如下：\n实数域上，x ◇ y = x + 5 □ 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: 3 % 1 ◇ 10 □ 2\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y - x + x + 3。
和 ◎，规则如下：
当x大于y时，x ◎ y = x ** y；
其他情况下，x ◎ y = x * y + 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: 4 ◎ 4 ☆ 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ☆，规则如下：\n实数域上，x ☆ y = y - x + x + 3。\n和 ◎，规则如下：\n当x大于y时，x ◎ y = x ** y；\n其他情况下，x ◎ y = x * y + 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: 4 ◎ 4 ☆ 4\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = abs(x) - x - y。
和 ☆，规则如下：
实数域上，x ☆ y = y + y * abs(x)。
和 ▽，规则如下：
当y是奇数时，x ▽ y = y - y ☆ x；
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: 4 ▽ 5 ⊕ 9 ☆ 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 = abs(x) - x - y。\n和 ☆，规则如下：\n实数域上，x ☆ y = y + y * abs(x)。\n和 ▽，规则如下：\n当y是奇数时，x ▽ y = y - y ☆ x；\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: 4 ▽ 5 ⊕ 9 ☆ 10\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x - y - y - 3 + 3。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ☆，规则如下：
当x是5的倍数时，x ☆ y = y + 1 * x；
其他情况下，x ☆ y = x + x - y。
和 ◎，规则如下：
当x和y都是奇数时，x ◎ y = abs(x + y) + y；
其他情况下，x ◎ y = x + (y - x)。
运算优先级：** > * = / = % = ☆ > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 - 9 ☆ 6 ◎ 2
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.
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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logic-v2 | 定义 △，规则如下：
实数域上，x △ y = x + 3 + abs(y) + x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8
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 = y / y - y ** x；
其他情况下，x ▽ y = 2 - y / 2 - x + 4。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = 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: 10 ▽ 3 - 4 - 4
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 - 3 * y + 3 / 3.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x + y - 5 / 4.
The precedence of operations: ** = □ > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ** 3 ◇ 1 - 5 □ 5
Please fill your final answer in \boxed{}. | {
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"⊙": null,
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " x - 3 * y + 3 / 3",
"precedence": 3
},
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y - 5 / 4",
"precedence": 2
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "facf5c52-a818-44c2-b7a4-d44b52fa9cda"
},
"question": "Define □, the rules are as follows:\non the real number field, x □ y = x - 3 * y + 3 / 3.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = x + y - 5 / 4.\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 ** 3 ◇ 1 - 5 □ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "9 ** 3 ◇ 1 - 5 □ 5",
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"numbers": null,
"operators": null,
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"seed": 20308148,
"simplified_expr": "((( ((9 ** 3)) + 1 - 5 / 4)) - (( 5 - 3 * 5 + 3 / 3)))",
"solutions_count": null,
"symbol_definitions": {
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"default_operation": " x - 3 * y + 3 / 3",
"precedence": 3
},
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y - 5 / 4",
"precedence": 2
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "facf5c52-a818-44c2-b7a4-d44b52fa9cda"
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"seed": 20308148,
"task_id": 220308148,
"task_type": "operation"
} |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y - abs(y + x) - x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * y + x + y ⊗ x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = y - x + 3 + x ⊗ y.
The precedence of operations: ** = ⊗ > * = / = % = ⊙ > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ♢ 4 ⊙ 10 ⊗ 9
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "11523",
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"gpt_response": "",
"metadata": {
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"expression": "3 ♢ 4 ⊙ 10 ⊗ 9",
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"seed": 283462,
"simplified_expr": "((((((((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * ((((((10 * 9)) - (abs((9 + 10))))) - 10)))) + 4)) + ((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * 4)) - (abs((4 + ((((((10 * 9)) - (abs((9 + 10))))) - 10))))))) - ((((((10 * 9)) - (abs((9 + 10))))) - 10)))))) - 3)) + 3)) + (( 3 * ((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * ((((((10 * 9)) - (abs((9 + 10))))) - 10)))) + 4)) + ((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * 4)) - (abs((4 + ((((((10 * 9)) - (abs((9 + 10))))) - 10))))))) - ((((((10 * 9)) - (abs((9 + 10))))) - 10)))))) - abs(((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * ((((((10 * 9)) - (abs((9 + 10))))) - 10)))) + 4)) + ((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * 4)) - (abs((4 + ((((((10 * 9)) - (abs((9 + 10))))) - 10))))))) - ((((((10 * 9)) - (abs((9 + 10))))) - 10)))))) + 3) - 3))))",
"solutions_count": null,
"symbol_definitions": {
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"⊗": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y - abs(y + x) - x",
"precedence": 3
},
"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y + x + y ⊗ x",
"precedence": 2
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x + 3 + x ⊗ y",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "157757a3-dc05-4185-b889-2e7a88a208ab"
},
"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = x * y - abs(y + x) - x.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = y * y + x + y ⊗ x.\nand ♢, the rules are as follows:\non the real number field, x ♢ y = y - x + 3 + x ⊗ y.\nThe precedence of operations: ** = ⊗ > * = / = % = ⊙ > + = - = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ♢ 4 ⊙ 10 ⊗ 9\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 4 ⊙ 10 ⊗ 9",
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"n_types": null,
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"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 283462,
"simplified_expr": "((((((((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * ((((((10 * 9)) - (abs((9 + 10))))) - 10)))) + 4)) + ((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * 4)) - (abs((4 + ((((((10 * 9)) - (abs((9 + 10))))) - 10))))))) - ((((((10 * 9)) - (abs((9 + 10))))) - 10)))))) - 3)) + 3)) + (( 3 * ((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * ((((((10 * 9)) - (abs((9 + 10))))) - 10)))) + 4)) + ((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * 4)) - (abs((4 + ((((((10 * 9)) - (abs((9 + 10))))) - 10))))))) - ((((((10 * 9)) - (abs((9 + 10))))) - 10)))))) - abs(((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * ((((((10 * 9)) - (abs((9 + 10))))) - 10)))) + 4)) + ((((((((((((10 * 9)) - (abs((9 + 10))))) - 10)) * 4)) - (abs((4 + ((((((10 * 9)) - (abs((9 + 10))))) - 10))))))) - ((((((10 * 9)) - (abs((9 + 10))))) - 10)))))) + 3) - 3))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y - abs(y + x) - x",
"precedence": 3
},
"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y + x + y ⊗ x",
"precedence": 2
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x + 3 + x ⊗ y",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "157757a3-dc05-4185-b889-2e7a88a208ab"
},
"seed": 283462,
"task_id": 200283462,
"task_type": "operation"
} |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x + y。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"expression": "3 ◇ 5",
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"○": null,
"◎": null,
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"♢": null
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"target": null,
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"trace_id": "dbeb6650-524c-42af-88f4-5ce111aff3e0"
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"question": "定义 ◇，规则如下：\n实数域上，x ◇ y = x + y。\n运算优先级：◇ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 ◇ 5\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 5",
"fill_length": null,
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"is_solvable": null,
"language": "chinese",
"n_types": null,
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"num_of_numbers": null,
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"operators": null,
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"seed": 51305762,
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"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y",
"precedence": 4
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "dbeb6650-524c-42af-88f4-5ce111aff3e0"
},
"seed": 51305762,
"task_id": 251305762,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, 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: 4 ** 5 ◇ 4
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "6140",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"expression": "4 ** 5 ◇ 4",
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"seed": 48512940,
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"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x + 5 * x - y",
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"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "7c4f8747-5653-4c53-8efa-7f635ed95862"
},
"question": "Define ◇, the rules are as follows:\non the real number field, x ◇ y = x + 5 * 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 ** 5 ◇ 4\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "4 ** 5 ◇ 4",
"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": 48512940,
"simplified_expr": "( ((4 ** 5)) + 5 * ((4 ** 5)) - 4)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x + 5 * x - y",
"precedence": 3
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "7c4f8747-5653-4c53-8efa-7f635ed95862"
},
"seed": 48512940,
"task_id": 248512940,
"task_type": "operation"
} |
logic-v2 | 定义 ○，规则如下：
当x大于y时，x ○ y = x * y - y；
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: 3 ○ 8 / 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.944444",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 8 / 6",
"fill_length": null,
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"simplified_expr": "((( 8 / 3 + 3)) / 6)",
"solutions_count": null,
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " x * y - y"
}
],
"default_operation": " y / x + x",
"precedence": 4
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "febb2de9-ff18-4c57-b0b3-31a27e8ed42b"
},
"question": "定义 ○，规则如下：\n当x大于y时，x ○ y = x * y - y；\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: 3 ○ 8 / 6\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 8 / 6",
"fill_length": null,
"full_sequence": null,
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 5892246,
"simplified_expr": "((( 8 / 3 + 3)) / 6)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " x * y - y"
}
],
"default_operation": " y / x + x",
"precedence": 4
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "febb2de9-ff18-4c57-b0b3-31a27e8ed42b"
},
"seed": 5892246,
"task_id": 205892246,
"task_type": "operation"
} |
logic-v2 | 定义 △，规则如下：
当x小于y时，x △ y = x + y + x；
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: 5 % 4 △ 10 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 % 4 △ 10 △ 6",
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"symbol_definitions": {
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"conditions": [
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"operation": " x + y + x"
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"default_operation": " y - y / x",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "fcec5e04-5e52-46be-b313-c91fcecd60ff"
},
"question": "定义 △，规则如下：\n当x小于y时，x △ y = x + y + x；\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: 5 % 4 △ 10 △ 6\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "5 % 4 △ 10 △ 6",
"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,
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"seed": 72158628,
"simplified_expr": "(5 % (( 6 - 6 / (( 4 + 10 + 4)))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [
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"condition": "x小于y",
"operation": " x + y + x"
}
],
"default_operation": " y - y / x",
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},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "fcec5e04-5e52-46be-b313-c91fcecd60ff"
},
"seed": 72158628,
"task_id": 272158628,
"task_type": "operation"
} |
logic-v2 | Define ⊙, the rules are as follows:
when x is even, x ⊙ y = y + x * x;
otherwise, x ⊙ y = x / y.
and ☆, the rules are as follows:
when the sum of x and y is odd, x ☆ y = y + x * y;
otherwise, x ☆ y = x * y - 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: 9 ☆ 9 ⊙ 2 △ 4
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "288",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 9 ⊙ 2 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
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"numbers": null,
"operators": null,
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"seed": 39299037,
"simplified_expr": "( (( 9 * 9 - 9)) / (( 2 / 4 / 2)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [
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"condition": "x是偶数",
"operation": " y + x * x"
}
],
"default_operation": " x / y",
"precedence": 3
},
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " x / y / x",
"precedence": 5
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是奇数",
"operation": " y + x * y"
}
],
"default_operation": " x * y - y",
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"question": "Define ⊙, the rules are as follows:\nwhen x is even, x ⊙ y = y + x * x;\notherwise, x ⊙ y = x / y.\nand ☆, the rules are as follows:\nwhen the sum of x and y is odd, x ☆ y = y + x * y;\notherwise, x ☆ y = x * y - 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: 9 ☆ 9 ⊙ 2 △ 4\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 △，规则如下：
实数域上，x △ y = x - y + x + y。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 % 1 △ 7
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 △，规则如下：
当x大于y时，x △ y = x / y * x；
其他情况下，x △ y = y * 2 + x。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 9 △ 1
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 less than y, x ⊕ y = x + 2 * y;
otherwise, x ⊕ y = x - x - y.
and ○, the rules are as follows:
when x is odd, x ○ y = x ⊕ (y);
otherwise, x ○ y = y + x + x.
and □, the rules are as follows:
on the real number field, x □ y = 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: 8 ○ 2 ⊕ 6 □ 10 + 10
Please fill your final answer in \boxed{}. | {
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},
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},
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"precedence": 2
},
"△": null,
"▽": null,
"◇": null,
"○": {
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"conditions": [
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],
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = 5 - y / x - y。
和 ◇，规则如下：
实数域上，x ◇ y = y + y * x - y ** x。
和 ▽，规则如下：
当x和y都是奇数时，x ▽ y = x + 3 + x + y ⊗ x；
其他情况下，x ▽ y = y - y - 1 * 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: 6 ▽ 8 ⊗ 6 ▽ 5 ◇ 5 - 9
请将最终答案填入\boxed{}中。 | {
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"default_operation": " y - y - 1 * x - x",
"precedence": 1
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"◇": {
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"default_operation": " y + y * x - y ** x",
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = 5 - y / x - y。\n和 ◇，规则如下：\n实数域上，x ◇ y = y + y * x - y ** x。\n和 ▽，规则如下：\n当x和y都是奇数时，x ▽ y = x + 3 + x + y ⊗ x；\n其他情况下，x ▽ y = y - y - 1 * 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: 6 ▽ 8 ⊗ 6 ▽ 5 ◇ 5 - 9\n请将最终答案填入\\boxed{}中。"
},
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"simplified_expr": "((( (( 5 + 5 * 5 - 5 ** 5)) - (( 5 + 5 * 5 - 5 ** 5)) - 1 * (( (( 5 - 6 / 8 - 6)) - (( 5 - 6 / 8 - 6)) - 1 * 6 - 6)) - (( (( 5 - 6 / 8 - 6)) - (( 5 - 6 / 8 - 6)) - 1 * 6 - 6)))) - 9)",
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],
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logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y - 1 / x - x。
和 ♡，规则如下：
当y是3的倍数时，x ♡ y = y + x；
其他情况下，x ♡ y = (x □ y)。
运算优先级：** = ♡ > * = / = % = □ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 2 ♡ 5 ♡ 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小于y时，x ◎ y = 1 - x + y - 5 / y；
其他情况下，x ◎ y = y * 4 + y - x。
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 * x + y * x * x。
运算优先级：◎ > ** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ○ 4 ◎ 7
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(x) - x * y - y * y；
其他情况下，x ☆ y = y ** x。
和 ◇，规则如下：
当x等于y时，x ◇ y = y ☆ x - 3；
其他情况下，x ◇ y = y + 1 ☆ x。
运算优先级：☆ = ◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ◇ 7
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 - x + (1 * 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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logic-v2 | Define ♢, the rules are as follows:
when the sum of x and y is even, x ♢ y = 4 + y + x / y + x;
otherwise, x ♢ y = x - x / y - x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = 1 * 3 * (x / y).
and ○, the rules are as follows:
when x is a multiple of 5, x ○ y = x + (x) / y;
otherwise, x ○ y = 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: 10 ♢ 9 ◎ 3
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ▽，规则如下：
当y是偶数时，x ▽ y = y - 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: 2 ▽ 9 % 4 + 5
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 less than y, x △ y = y + x - 2 + 5;
otherwise, x △ y = 1 - 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 / 4 △ 2
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 + 5 - x + x + y。
和 ○，规则如下：
当x和y都是奇数时，x ○ y = (y * y + x) ** y * x；
其他情况下，x ○ y = y ⊙ (x - y) / x。
和 ⊕，规则如下：
实数域上，x ⊕ y = (x - 2 + 5 * 2) + y。
运算优先级：⊙ = ○ > ⊕ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ○ 5 ⊙ 6 ⊕ 2
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ⊙，规则如下：
当x和y都是偶数时，x ⊙ y = x + y；
其他情况下，x ⊙ y = x * y。
和 □，规则如下：
当y是奇数时，x □ y = y * y - x；
其他情况下，x □ y = y - abs(x - y)。
和 ♢，规则如下：
当x是偶数时，x ♢ y = x * 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: 3 ⊙ 3 ♢ 10
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ♢，规则如下：
当x等于y时，x ♢ y = y * y + y ** x + 3；
其他情况下，x ♢ y = y * x * 4。
和 ⊗，规则如下：
实数域上，x ⊗ y = x - x - y。
和 ♡，规则如下：
实数域上，x ♡ y = 2 - 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 ⊗ 6 ♡ 4
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ♡，规则如下：
当x是偶数时，x ♡ y = x + y - y；
其他情况下，x ♡ y = y * x + (2)。
和 ☆，规则如下：
实数域上，x ☆ y = y + abs(y + x)。
运算优先级：♡ > ** = ☆ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ☆ 9 - 9 ♡ 10
请将最终答案填入\boxed{}中。 | {
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"♢": null
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logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y * y * x + y.
and □, the rules are as follows:
on the real number field, x □ y = 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 ♡ 2
Please fill your final answer in \boxed{}. | {
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"precedence": 1
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"△": null,
"▽": null,
"◇": null,
"○": 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 odd, x ▽ y = y * y * x;
otherwise, 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: 4
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x + abs(x) / y。
和 ○，规则如下：
实数域上，x ○ y = y + x - 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: 2 ⊗ 5 ♡ 9 ○ 2
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | Define ☆, the rules are as follows:
when x and y are both even, x ☆ y = y ** y * x - y;
otherwise, x ☆ y = x * y - (x - y).
and ♡, the rules are as follows:
on the real number field, x ♡ y = x - y - 4 ☆ y.
The precedence of operations: ♡ > ** > * = / = % = ☆ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ♡ 1
Please fill your final answer in \boxed{}. | {
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"♢": null
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},
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x / y。
和 △，规则如下：
当x和y都是偶数时，x △ y = 1 + y * x；
其他情况下，x △ y = x ⊗ x - y。
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: 1 ♢ 8 ⊗ 9
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y + (4 * 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
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ◎，规则如下：
当y是5的倍数时，x ◎ y = y - x + x；
其他情况下，x ◎ y = x + y。
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: 8 △ 10 ◎ 5
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) ** x - x / y。
和 ○，规则如下：
实数域上，x ○ y = 2 + 5 + 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: 6 □ 1 ○ 8 % 2 - 7
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | Define ⊗, the rules are as follows:
when the sum of x and y is even, x ⊗ y = y + y + x;
otherwise, x ⊗ y = y * x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y + x + y.
and ▽, the rules are as follows:
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: 2 ♡ 1 ⊗ 1 ▽ 3
Please fill your final answer in \boxed{}. | {
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"○": null,
"◎": null,
"☆": null,
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"associativity": "left",
"conditions": [],
"default_operation": " y + x + y",
"precedence": 3
},
"♢": null
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},
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"○": null,
"◎": null,
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"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x + y",
"precedence": 3
},
"♢": null
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} |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y + x / y。
和 △，规则如下：
实数域上，x △ y = x - y ⊙ y + 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: 7 △ 1 ⊙ 8 ☆ 9
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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"question": "定义 ⊙，规则如下：\n实数域上，x ⊙ y = y + x / y。\n和 △，规则如下：\n实数域上，x △ y = x - y ⊙ y + x。\n和 ☆，规则如下：\n实数域上，x ☆ y = (y) + x。\n运算优先级：△ > ** = ☆ > * = / = % > + = - = ⊙。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 7 △ 1 ⊙ 8 ☆ 9\n请将最终答案填入\\boxed{}中。"
},
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"seed": 54454119,
"simplified_expr": "( (( (9) + 8)) + ((((( 1 + ((7 - 1)) / 1)) + 7))) / (( (9) + 8)))",
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"◇": null,
"○": null,
"◎": null,
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"associativity": "left",
"conditions": [],
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"precedence": 3
},
"♡": null,
"♢": null
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"seed": 54454119,
"task_id": 254454119,
"task_type": "operation"
} |
logic-v2 | Define ⊕, the rules are as follows:
when x is equal to y, x ⊕ y = x * y + 3 * x * x;
otherwise, x ⊕ y = x / x - x - x ** y.
and ◎, the rules are as follows:
when x is equal to y, x ◎ y = y * y + x ⊕ x;
otherwise, x ◎ y = y / (y + x + 3).
and ◇, the rules are as follows:
on the real number field, x ◇ y = 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: 5 ⊕ 4 ◎ 6 ◇ 1
Please fill your final answer in \boxed{}. | {
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"○": null,
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"conditions": [
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"condition": "x等于y",
"operation": " y * y + x ⊕ x"
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],
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"☆": null,
"♡": null,
"♢": null
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"target": null,
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"question": "Define ⊕, the rules are as follows:\nwhen x is equal to y, x ⊕ y = x * y + 3 * x * x;\notherwise, x ⊕ y = x / x - x - x ** y.\nand ◎, the rules are as follows:\nwhen x is equal to y, x ◎ y = y * y + x ⊕ x;\notherwise, x ◎ y = y / (y + x + 3).\nand ◇, the rules are as follows:\non the real number field, x ◇ y = 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: 5 ⊕ 4 ◎ 6 ◇ 1\nPlease fill your final answer in \\boxed{}."
},
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"○": null,
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"conditions": [
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"condition": "x等于y",
"operation": " y * y + x ⊕ x"
}
],
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"☆": null,
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logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y + x + 3 - 3.
and ○, the rules are as follows:
when x is less than y, x ○ y = y + y □ x - 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: 4 ○ 9 □ 1
Please fill your final answer in \boxed{}. | {
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"☆": 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 + 3 - 3.\nand ○, the rules are as follows:\nwhen x is less than y, x ○ y = y + y □ x - 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: 4 ○ 9 □ 1\nPlease 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 = x + x + y；
其他情况下，x ☆ y = y / y + x * y。
和 ○，规则如下：
实数域上，x ○ y = x / (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: 6 ○ 1 - 7 ☆ 8
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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"question": "定义 ☆，规则如下：\n当x是3的倍数时，x ☆ y = x + x + y；\n其他情况下，x ☆ y = y / y + x * y。\n和 ○，规则如下：\n实数域上，x ○ y = x / (x ☆ 3 + 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 ○ 1 - 7 ☆ 8\n请将最终答案填入\\boxed{}中。"
},
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"condition": "x是3的倍数",
"operation": " x + x + y"
}
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"♢": null
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},
"seed": 10738927,
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} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x + y - x.
and ◇, the rules are as follows:
when y is even, x ◇ y = y - x - y;
otherwise, x ◇ y = x * y ** y.
The precedence of operations: ◇ > ** > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ◇ 1 + 9 ☆ 1
Please fill your final answer in \boxed{}. | {
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},
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},
"target": null,
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"trace_id": "15201e3d-d1e3-42b7-a164-58ae3fb0d721"
},
"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = x + y - x.\nand ◇, the rules are as follows:\nwhen y is even, x ◇ y = y - x - y;\notherwise, x ◇ y = x * y ** y.\nThe precedence of operations: ◇ > ** > * = / = % > + = - = ☆。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ◇ 1 + 9 ☆ 1\nPlease fill your final answer in \\boxed{}."
},
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"seed": 48866295,
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} |
logic-v2 | 定义 △，规则如下：
当x和y的和是奇数时，x △ y = x * x + x - y / x；
其他情况下，x △ y = x * y。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 △ 2
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 = x * x + x - y / x；\n其他情况下，x △ y = x * y。\n运算优先级：** > * = / = % = △ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 △ 2\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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logic-v2 | 定义 △，规则如下：
当y是5的倍数时，x △ y = abs(x + y)；
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: 3
请将最终答案填入\boxed{}中。 | {
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"question": "定义 △，规则如下：\n当y是5的倍数时，x △ y = abs(x + y)；\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: 3\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 40533326,
"simplified_expr": "3",
"solutions_count": null,
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"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " abs(x + y)"
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"precedence": 5
},
"▽": null,
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"○": null,
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"seed": 40533326,
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} |
logic-v2 | Define ▽, the rules are as follows:
when x is a multiple of 5, x ▽ y = abs(y) - y + x + x;
otherwise, x ▽ y = x + x - y.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ▽ 7 ** 1
Please fill your final answer in \boxed{}. | {
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"question": "Define ▽, the rules are as follows:\nwhen x is a multiple of 5, x ▽ y = abs(y) - y + x + x;\notherwise, x ▽ y = x + x - y.\nThe precedence of operations: ** > * = / = % = ▽ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 ▽ 7 ** 1\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
{
"condition": "x是5的倍数",
"operation": " abs(y) - y + x + x"
}
],
"default_operation": " x + x - y",
"precedence": 2
},
"◇": null,
"○": null,
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},
"seed": 32217130,
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} |
logic-v2 | 定义 ⊗，规则如下：
当x是偶数时，x ⊗ y = x + abs(y)；
其他情况下，x ⊗ y = x + x * y。
和 □，规则如下：
当x大于y时，x □ y = x ⊗ y；
其他情况下，x □ y = (x) + y。
和 ○，规则如下：
当y是5的倍数时，x ○ y = y □ x - y；
其他情况下，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: 8 □ 7 ○ 10 ⊗ 4
请将最终答案填入\boxed{}中。 | {
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"answer": "1380",
"difficulty": 1,
"gpt_response": "",
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"conditions": [
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"condition": "x大于y",
"operation": " x ⊗ y"
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],
"default_operation": " (x) + y",
"precedence": 1
},
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " y □ x - y"
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],
"default_operation": " y * x * y",
"precedence": 2
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"question": "定义 ⊗，规则如下：\n当x是偶数时，x ⊗ y = x + abs(y)；\n其他情况下，x ⊗ y = x + x * y。\n和 □，规则如下：\n当x大于y时，x □ y = x ⊗ y；\n其他情况下，x □ y = (x) + y。\n和 ○，规则如下：\n当y是5的倍数时，x ○ y = y □ x - y；\n其他情况下，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: 8 □ 7 ○ 10 ⊗ 4\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "8 □ 7 ○ 10 ⊗ 4",
"fill_length": null,
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"seed": 683129,
"simplified_expr": "( (8) + (( (( 10 + abs(4))) * 7 * (( 10 + abs(4))))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [
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"condition": "x是偶数",
"operation": " x + abs(y)"
}
],
"default_operation": " x + x * y",
"precedence": 3
},
"⊙": null,
"□": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " x ⊗ y"
}
],
"default_operation": " (x) + y",
"precedence": 1
},
"△": null,
"▽": null,
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"○": {
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"conditions": [
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}
],
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"precedence": 2
},
"◎": null,
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"♢": null
},
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},
"seed": 683129,
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} |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = (y + x * x)。
和 ☆，规则如下：
当y是偶数时，x ☆ y = y / y + x；
其他情况下，x ☆ y = y + x。
和 ⊕，规则如下：
当x是偶数时，x ⊕ y = y ** y ♢ x；
其他情况下，x ⊕ y = x * y。
运算优先级：** = ♢ = ☆ > * = / = % = ⊕ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ⊕ 3 ♢ 10 ☆ 8
请将最终答案填入\boxed{}中。 | {
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"◎": null,
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"conditions": [
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"condition": "y是偶数",
"operation": " y / y + x"
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"default_operation": " y + x",
"precedence": 3
},
"♡": null,
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"associativity": "left",
"conditions": [],
"default_operation": " (y + x * x)",
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},
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"⊙": null,
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"△": null,
"▽": null,
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"☆": {
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"conditions": [
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"default_operation": " y + x",
"precedence": 3
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " (y + x * x)",
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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) * y。
和 △，规则如下：
实数域上，x △ y = y + x * x。
运算优先级：□ > ** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 □ 7 △ 6 △ 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小于y时，x ⊙ y = x * y + x - 3；
其他情况下，x ⊙ y = (y + x)。
和 ♡，规则如下：
实数域上，x ♡ y = y * x - y ⊙ y。
和 ⊗，规则如下：
当y是3的倍数时，x ⊗ y = x * y ⊙ y；
其他情况下，x ⊗ y = y / 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: 4 ⊗ 4 ♡ 8 ⊙ 9
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = (y ** x) * y。
和 ◎，规则如下：
当x是5的倍数时，x ◎ y = y ⊙ x ** x；
其他情况下，x ◎ y = x * y。
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 ◎ 3 ⊙ 1
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 * x - y。
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 - 3 ⊙ 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: 10 △ 3 ⊙ 4 ☆ 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。\n和 ⊙，规则如下：\n实数域上，x ⊙ y = y + x - x。\n和 △，规则如下：\n实数域上，x △ y = x - 3 ⊙ 3 + y。\n运算优先级：** = ☆ = ⊙ > * = / = % > + = - = △。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 △ 3 ⊙ 4 ☆ 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 - y.
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: 3 ◎ 10
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 = y * y / x.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 + 9 ▽ 9 ▽ 7
Please fill your final answer in \boxed{}. | {
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logic-v2 | Define ⊕, the rules are as follows:
when x and y are both odd, x ⊕ y = y - x * y;
otherwise, x ⊕ y = x + y.
and ◎, the rules are as follows:
when x is greater than y, x ◎ y = x + x ⊕ y;
otherwise, x ◎ y = y ⊕ x.
and ☆, the rules are as follows:
when x is a multiple of 5, x ☆ y = 3 * (y ◎ x);
otherwise, x ☆ y = 2 ◎ 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 ☆ 7 ⊕ 10 ◎ 4
Please fill your final answer in \boxed{}. | {
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"default_operation": " y ⊕ x",
"precedence": 3
},
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x是5的倍数",
"operation": " 3 * (y ◎ x)"
}
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"default_operation": " 2 ◎ x + y",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
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"question": "Define ⊕, the rules are as follows:\nwhen x and y are both odd, x ⊕ y = y - x * y;\notherwise, x ⊕ y = x + y.\nand ◎, the rules are as follows:\nwhen x is greater than y, x ◎ y = x + x ⊕ y;\notherwise, x ◎ y = y ⊕ x.\nand ☆, the rules are as follows:\nwhen x is a multiple of 5, x ☆ y = 3 * (y ◎ x);\notherwise, x ☆ y = 2 ◎ 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 ☆ 7 ⊕ 10 ◎ 4\nPlease fill your final answer in \\boxed{}."
},
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"conditions": [
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"operation": " x + x ⊕ y"
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],
"default_operation": " y ⊕ x",
"precedence": 3
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"☆": {
"associativity": "left",
"conditions": [
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"condition": "x是5的倍数",
"operation": " 3 * (y ◎ x)"
}
],
"default_operation": " 2 ◎ x + y",
"precedence": 5
},
"♡": null,
"♢": null
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"seed": 43829650,
"task_id": 243829650,
"task_type": "operation"
} |
logic-v2 | Define △, the rules are as follows:
when x is even, x △ y = y + x * x;
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{}. | {
"game_data": {
"answer": "8",
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"gpt_response": "",
"metadata": {
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"expression": "8",
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"question": "Define △, the rules are as follows:\nwhen x is even, x △ y = y + x * x;\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": {
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"expression": "8",
"fill_length": null,
"full_sequence": null,
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"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
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"simplified_expr": "8",
"solutions_count": null,
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"⊗": null,
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"△": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " y + x * x"
}
],
"default_operation": " y - x + y",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"target": null,
"total_length": null,
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} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = 1 + y + x.
and ♢, the rules are as follows:
when x is even, x ♢ y = (x + x) ☆ y / x;
otherwise, 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: 9 ♢ 10
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "19",
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"operation": " (x + x) ☆ y / x"
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"default_operation": " y + y + (x - y)",
"precedence": 4
}
},
"target": null,
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"trace_id": "68a6b818-2e63-4703-80f1-a29836c4d67c"
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = 1 + y + x.\nand ♢, the rules are as follows:\nwhen x is even, x ♢ y = (x + x) ☆ y / x;\notherwise, 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: 9 ♢ 10\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "9 ♢ 10",
"fill_length": null,
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"operators": null,
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"seed": 50767647,
"simplified_expr": "( 10 + 10 + (9 - 10))",
"solutions_count": null,
"symbol_definitions": {
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " 1 + y + x",
"precedence": 5
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
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"condition": "x是偶数",
"operation": " (x + x) ☆ y / x"
}
],
"default_operation": " y + y + (x - y)",
"precedence": 4
}
},
"target": null,
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"trace_id": "68a6b818-2e63-4703-80f1-a29836c4d67c"
},
"seed": 50767647,
"task_id": 250767647,
"task_type": "operation"
} |
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: 4 % 1 - 7 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
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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: 4 % 1 - 7 ▽ 7\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"seed": 59801613,
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} |
logic-v2 | Define ◎, the rules are as follows:
when x is greater than y, x ◎ y = (x * y * y) * x ** x;
otherwise, x ◎ y = (y + x) + 1.
and △, the rules are as follows:
when x and y are both odd, x △ y = x + x - y ◎ y / y;
otherwise, x △ y = 2 - x * 2 * 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 ◎ 6
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "10",
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"gpt_response": "",
"metadata": {
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"expression": "3 ◎ 6",
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"num_symbols": 2,
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"operators": null,
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"seed": 7033918,
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"symbol_definitions": {
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"□": null,
"△": {
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],
"default_operation": " 2 - x * 2 * y ◎ y",
"precedence": 5
},
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [
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"condition": "x大于y",
"operation": " (x * y * y) * x ** x"
}
],
"default_operation": " (y + x) + 1",
"precedence": 3
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "435f8fdf-3023-4073-9e81-c884bfd4f786"
},
"question": "Define ◎, the rules are as follows:\nwhen x is greater than y, x ◎ y = (x * y * y) * x ** x;\notherwise, x ◎ y = (y + x) + 1.\nand △, the rules are as follows:\nwhen x and y are both odd, x △ y = x + x - y ◎ y / y;\notherwise, x △ y = 2 - x * 2 * 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 ◎ 6\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "3 ◎ 6",
"fill_length": null,
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"is_solvable": null,
"language": "english",
"n_types": null,
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"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 7033918,
"simplified_expr": "( (6 + 3) + 1)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
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"conditions": [
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"condition": "x和y都是奇数",
"operation": " x + x - y ◎ y / y"
}
],
"default_operation": " 2 - x * 2 * y ◎ y",
"precedence": 5
},
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " (x * y * y) * x ** x"
}
],
"default_operation": " (y + x) + 1",
"precedence": 3
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "435f8fdf-3023-4073-9e81-c884bfd4f786"
},
"seed": 7033918,
"task_id": 207033918,
"task_type": "operation"
} |
logic-v2 | Define □, the rules are as follows:
when x and y are both odd, x □ y = x - y - y - 2;
otherwise, x □ y = y + x / y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = 2 + (4 □ 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 □ 3
Please fill your final answer in \boxed{}. | {
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"num_symbols": 2,
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"operators": null,
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"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": {
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"conditions": [],
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"precedence": 3
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"□": {
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"conditions": [
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"operation": " x - y - y - 2"
}
],
"default_operation": " y + x / y",
"precedence": 5
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "406b327d-e793-4ba7-b598-ae697708cbc5"
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"question": "Define □, the rules are as follows:\nwhen x and y are both odd, x □ y = x - y - y - 2;\notherwise, x □ y = y + x / y.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = 2 + (4 □ 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 □ 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "3 □ 3",
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"is_solvable": null,
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"num_of_numbers": null,
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"operators": null,
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"seed": 87161530,
"simplified_expr": "( 3 - 3 - 3 - 2)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " 2 + (4 □ y) ** x",
"precedence": 3
},
"□": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " x - y - y - 2"
}
],
"default_operation": " y + x / y",
"precedence": 5
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "406b327d-e793-4ba7-b598-ae697708cbc5"
},
"seed": 87161530,
"task_id": 287161530,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
when y is a multiple of 5, x ▽ y = y ** x;
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: 8 ▽ 7 ▽ 10
Please fill your final answer in \boxed{}. | {
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],
"default_operation": " y - x - x",
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},
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"question": "Define ▽, the rules are as follows:\nwhen y is a multiple of 5, x ▽ y = y ** x;\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: 8 ▽ 7 ▽ 10\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define ♢, the rules are as follows:
when x is even, x ♢ y = abs(y + y - x);
otherwise, x ♢ y = y + y + x.
and △, the rules are as follows:
when y is a multiple of 3, x △ y = y ♢ (y + x);
otherwise, x △ y = y - x + y.
and ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = x * y - y;
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 ⊗ 3 △ 6 ♢ 9
Please fill your final answer in \boxed{}. | {
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"precedence": 5
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"♢": {
"associativity": "left",
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"condition": "x是偶数",
"operation": " abs(y + y - x)"
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"default_operation": " y + y + x",
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}
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"question": "Define ♢, the rules are as follows:\nwhen x is even, x ♢ y = abs(y + y - x);\notherwise, x ♢ y = y + y + x.\nand △, the rules are as follows:\nwhen y is a multiple of 3, x △ y = y ♢ (y + x);\notherwise, x △ y = y - x + y.\nand ⊗, the rules are as follows:\nwhen x is greater than y, x ⊗ y = x * y - y;\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 ⊗ 3 △ 6 ♢ 9\nPlease fill your final answer in \\boxed{}."
},
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"○": null,
"◎": null,
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} |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = abs(y + x) * y。
运算优先级：** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 + 5 ○ 1 ○ 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 = abs(y + x) * y。\n运算优先级：** = ○ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 + 5 ○ 1 ○ 9\n请将最终答案填入\\boxed{}中。"
},
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} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y - y - x.
and △, the rules are as follows:
when x and y are both odd, x △ y = x * y;
otherwise, x △ y = x ◎ y + x.
The precedence of operations: ** = ◎ = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ◎ 5
Please fill your final answer in \boxed{}. | {
"game_data": {
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = y - y - x.\nand △, the rules are as follows:\nwhen x and y are both odd, x △ y = x * y;\notherwise, x △ y = x ◎ y + x.\nThe precedence of operations: ** = ◎ = △ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ◎ 5\nPlease fill your final answer in \\boxed{}."
},
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"seed": 59687482,
"simplified_expr": "( 5 - 5 - 5)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
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"seed": 59687482,
"task_id": 259687482,
"task_type": "operation"
} |
logic-v2 | 定义 ☆，规则如下：
当x和y都是奇数时，x ☆ y = x - x + x * y；
其他情况下，x ☆ y = y + x * y + abs(1 - x)。
和 □，规则如下：
实数域上，x □ y = 3 / x ☆ y * 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: 8 ☆ 10 □ 9 - 3
请将最终答案填入\boxed{}中。 | {
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"operation": " x - x + x * y"
}
],
"default_operation": " y + x * y + abs(1 - x)",
"precedence": 1
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "40c70b3b-2caa-4777-bfff-8759cd3c4387"
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"question": "定义 ☆，规则如下：\n当x和y都是奇数时，x ☆ y = x - x + x * y；\n其他情况下，x ☆ y = y + x * y + abs(1 - x)。\n和 □，规则如下：\n实数域上，x □ y = 3 / x ☆ y * 1。\n运算优先级：** > * = / = % > + = - = ☆ = □。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 ☆ 10 □ 9 - 3\n请将最终答案填入\\boxed{}中。"
},
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"○": null,
"◎": null,
"☆": {
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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.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ○ 7
Please fill your final answer in \boxed{}. | {
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},
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} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x * 3 - y.
and ♡, the rules are as follows:
when x is equal to y, x ♡ y = y ◎ (y - y * x);
otherwise, x ♡ y = y - x ◎ x + 4.
The precedence of operations: ◎ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ♡ 2
Please fill your final answer in \boxed{}. | {
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"♢": null
},
"target": null,
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = x * 3 - y.\nand ♡, the rules are as follows:\nwhen x is equal to y, x ♡ y = y ◎ (y - y * x);\notherwise, x ♡ y = y - x ◎ x + 4.\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 ♡ 2\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 △，规则如下：
实数域上，x △ y = 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 △ 3 * 4 ** 2
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 = 1 - y - 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: 1 △ 9 ** 2 * 3
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y * x * y * 2.
and □, the rules are as follows:
on the real number field, x □ y = 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: 7 △ 2 □ 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 * 2.\nand □, the rules are as follows:\non the real number field, x □ y = 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: 7 △ 2 □ 2\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 ♡，规则如下：
当y是偶数时，x ♡ y = y + x + (x) + 4 + y；
其他情况下，x ♡ y = x + x + y - x - x。
和 ◇，规则如下：
实数域上，x ◇ y = x - 1 - 5 + y / 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: 6 - 1 ◇ 10 ♡ 1
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ♡，规则如下：\n当y是偶数时，x ♡ y = y + x + (x) + 4 + y；\n其他情况下，x ♡ y = x + x + y - x - x。\n和 ◇，规则如下：\n实数域上，x ◇ y = x - 1 - 5 + y / 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: 6 - 1 ◇ 10 ♡ 1\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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],
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"♢": null
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} |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y + 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: 8
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | 定义 △，规则如下：
当x是5的倍数时，x △ y = x * y；
其他情况下，x △ y = y - x * y * x。
和 ⊕，规则如下：
实数域上，x ⊕ y = 5 / y - x * x + x。
和 ▽，规则如下：
当x小于y时，x ▽ y = x △ x / y / y；
其他情况下，x ▽ y = x - x / 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: 7 ⊕ 6 ⊕ 6 △ 8 ▽ 7
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；\n其他情况下，x △ y = y - x * y * x。\n和 ⊕，规则如下：\n实数域上，x ⊕ y = 5 / y - x * x + x。\n和 ▽，规则如下：\n当x小于y时，x ▽ y = x △ x / y / y；\n其他情况下，x ▽ y = x - x / 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: 7 ⊕ 6 ⊕ 6 △ 8 ▽ 7\n请将最终答案填入\\boxed{}中。"
},
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},
"▽": {
"associativity": "left",
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"operation": " x △ x / y / y"
}
],
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},
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} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = abs(x * y).
and □, the rules are as follows:
when the sum of x and y is odd, x □ y = y ☆ x + y;
otherwise, x □ y = x ☆ y * 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 □ 2 * 1 □ 10 ☆ 7
Please fill your final answer in \boxed{}. | {
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"expression": "9 □ 2 * 1 □ 10 ☆ 7",
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"simplified_expr": "(((( abs((((abs((((2 * 1)) * 9))) + ((2 * 1)))) * (abs((10 * 7)))))) * (((abs((((2 * 1)) * 9))) + ((2 * 1))))))",
"solutions_count": null,
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"operation": " y ☆ x + y"
}
],
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},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " abs(x * y)",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = abs(x * y).\nand □, the rules are as follows:\nwhen the sum of x and y is odd, x □ y = y ☆ x + y;\notherwise, x □ y = x ☆ y * 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 □ 2 * 1 □ 10 ☆ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "9 □ 2 * 1 □ 10 ☆ 7",
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"seed": 58825943,
"simplified_expr": "(((( abs((((abs((((2 * 1)) * 9))) + ((2 * 1)))) * (abs((10 * 7)))))) * (((abs((((2 * 1)) * 9))) + ((2 * 1))))))",
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"operation": " y ☆ x + y"
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"▽": null,
"◇": null,
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"☆": {
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"♢": null
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"seed": 58825943,
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logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x ** y - y.
and ○, the rules are as follows:
when the sum of x and y is odd, x ○ y = x ** y + y;
otherwise, x ○ y = x + y ⊙ x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y + x - y.
The precedence of operations: ○ > ** > * = / = % = ◇ > + = - = ⊙。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ⊙ 6 ◇ 1 ○ 8 ○ 6
Please fill your final answer in \boxed{}. | {
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"difficulty": 1,
"gpt_response": "",
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"expression": "2 ⊙ 6 ◇ 1 ○ 8 ○ 6",
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"seed": 19267462,
"simplified_expr": "( 2 ** (( (( (( 1 ** 8 + 8)) ** 6 + 6)) + 6 - (( (( 1 ** 8 + 8)) ** 6 + 6)))) - (( (( (( 1 ** 8 + 8)) ** 6 + 6)) + 6 - (( (( 1 ** 8 + 8)) ** 6 + 6)))))",
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"precedence": 1
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"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x - y",
"precedence": 2
},
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是奇数",
"operation": " x ** y + y"
}
],
"default_operation": " x + y ⊙ x",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "aff038db-7ce5-4b1a-a42c-b386e6fa8cea"
},
"question": "Define ⊙, the rules are as follows:\non the real number field, x ⊙ y = x ** y - y.\nand ○, the rules are as follows:\nwhen the sum of x and y is odd, x ○ y = x ** y + y;\notherwise, x ○ y = x + y ⊙ x.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = y + x - y.\nThe precedence of operations: ○ > ** > * = / = % = ◇ > + = - = ⊙。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ⊙ 6 ◇ 1 ○ 8 ○ 6\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 6 ◇ 1 ○ 8 ○ 6",
"fill_length": null,
"full_sequence": null,
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"language": "english",
"n_types": null,
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"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 19267462,
"simplified_expr": "( 2 ** (( (( (( 1 ** 8 + 8)) ** 6 + 6)) + 6 - (( (( 1 ** 8 + 8)) ** 6 + 6)))) - (( (( (( 1 ** 8 + 8)) ** 6 + 6)) + 6 - (( (( 1 ** 8 + 8)) ** 6 + 6)))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " x ** y - y",
"precedence": 1
},
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x - y",
"precedence": 2
},
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是奇数",
"operation": " x ** y + y"
}
],
"default_operation": " x + y ⊙ x",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "aff038db-7ce5-4b1a-a42c-b386e6fa8cea"
},
"seed": 19267462,
"task_id": 219267462,
"task_type": "operation"
} |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x - x * y。
和 ○，规则如下：
当x是3的倍数时，x ○ y = x + y - y - x + y；
其他情况下，x ○ y = y * x - abs(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 ☆ 3 ○ 3 ** 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1136.419753",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 24778251,
"simplified_expr": "( ((3 ** 4)) * (( 7 - 7 * 3)) - abs((( 7 - 7 * 3)) / ((3 ** 4)) * (( 7 - 7 * 3))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " x + y - y - x + y"
}
],
"default_operation": " y * x - abs(x / y * x)",
"precedence": 2
},
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x - x * y",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "9f582c01-792f-4be3-8843-6511e741ae23"
},
"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是3的倍数时，x ○ y = x + y - y - x + y；\n其他情况下，x ○ y = y * x - abs(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: 7 ☆ 3 ○ 3 ** 4\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "7 ☆ 3 ○ 3 ** 4",
"fill_length": null,
"full_sequence": null,
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"n_types": null,
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"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 24778251,
"simplified_expr": "( ((3 ** 4)) * (( 7 - 7 * 3)) - abs((( 7 - 7 * 3)) / ((3 ** 4)) * (( 7 - 7 * 3))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " x + y - y - x + y"
}
],
"default_operation": " y * x - abs(x / y * x)",
"precedence": 2
},
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x - x * y",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "9f582c01-792f-4be3-8843-6511e741ae23"
},
"seed": 24778251,
"task_id": 224778251,
"task_type": "operation"
} |
logic-v2 | 定义 ☆，规则如下：
当x和y都是偶数时，x ☆ y = y + x；
其他情况下，x ☆ y = y * y ** x。
和 △，规则如下：
实数域上，x △ y = y / x ☆ x。
运算优先级：☆ > ** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 △ 4 ☆ 5 / 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "195.3125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 4 ☆ 5 / 1",
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"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 66749837,
"simplified_expr": "((((((5 * ((5 ** 4)))) / (( 8 + 8))))) / 1)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
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"conditions": [],
"default_operation": " y / x ☆ x",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " y + x"
}
],
"default_operation": " y * y ** x",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "864642b0-a4c1-4ee8-9781-65ec9d7a9c8d"
},
"question": "定义 ☆，规则如下：\n当x和y都是偶数时，x ☆ y = y + x；\n其他情况下，x ☆ y = y * y ** x。\n和 △，规则如下：\n实数域上，x △ y = y / x ☆ x。\n运算优先级：☆ > ** = △ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 △ 4 ☆ 5 / 1\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "8 △ 4 ☆ 5 / 1",
"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": 66749837,
"simplified_expr": "((((((5 * ((5 ** 4)))) / (( 8 + 8))))) / 1)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x ☆ x",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " y + x"
}
],
"default_operation": " y * y ** x",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "864642b0-a4c1-4ee8-9781-65ec9d7a9c8d"
},
"seed": 66749837,
"task_id": 266749837,
"task_type": "operation"
} |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x + y * 4 * 4。
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: 6 ♡ 7 ○ 4 - 1 * 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "112",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 7 ○ 4 - 1 * 6",
"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": 40130154,
"simplified_expr": "((( 6 + ((((( 7 + 7 * 4 * 4)) - ((((4 * 7)) * 4))))) * 4 * 4)) - ((1 * 6)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x ♡ x - y * x * y",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y * 4 * 4",
"precedence": 2
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "010544d6-c633-44e2-9e65-28640bc97aab"
},
"question": "定义 ♡，规则如下：\n实数域上，x ♡ y = x + y * 4 * 4。\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: 6 ♡ 7 ○ 4 - 1 * 6\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 7 ○ 4 - 1 * 6",
"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": 40130154,
"simplified_expr": "((( 6 + ((((( 7 + 7 * 4 * 4)) - ((((4 * 7)) * 4))))) * 4 * 4)) - ((1 * 6)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x ♡ x - y * x * y",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y * 4 * 4",
"precedence": 2
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "010544d6-c633-44e2-9e65-28640bc97aab"
},
"seed": 40130154,
"task_id": 240130154,
"task_type": "operation"
} |
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