env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ◇，规则如下：
当x是偶数时，x ◇ y = y - x * x；
其他情况下，x ◇ y = x - y * x。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◇ 1
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◇，规则如下：\n当x是偶数时，x ◇ y = y - x * x；\n其他情况下，x ◇ y = x - y * x。\n运算优先级：** > * = / = % > + = - = ◇。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 ◇ 1\n请将最终答案填入\\boxed{}中。"
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"◇": {
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logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x * 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
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◇，规则如下：\n实数域上，x ◇ y = x * y * x。\n运算优先级：** > * = / = % = ◇ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 7\n请将最终答案填入\\boxed{}中。"
},
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"symbol_definitions": {
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"◇": {
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"○": null,
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logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y + y * (x + x)。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ▽ 9 % 8
请将最终答案填入\boxed{}中。 | {
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"answer": "15",
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"expression": "7 ▽ 9 % 8",
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"numbers": null,
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"seed": 69649986,
"simplified_expr": "( ((9 % 8)) + ((9 % 8)) * (7 + 7))",
"solutions_count": null,
"symbol_definitions": {
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"♢": null
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"question": "定义 ▽，规则如下：\n实数域上，x ▽ y = y + y * (x + x)。\n运算优先级：** > * = / = % > + = - = ▽。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 7 ▽ 9 % 8\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 9 % 8",
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"numbers": null,
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"seed": 69649986,
"simplified_expr": "( ((9 % 8)) + ((9 % 8)) * (7 + 7))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
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"▽": {
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"conditions": [],
"default_operation": " y + y * (x + x)",
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"◇": null,
"○": null,
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"seed": 69649986,
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} |
logic-v2 | Define ○, the rules are as follows:
when the sum of x and y is even, x ○ y = x - abs(y + x);
otherwise, x ○ y = x * y.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ○ 10 ○ 7
Please fill your final answer in \boxed{}. | {
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"gpt_response": "",
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"expression": "9 ○ 10 ○ 7",
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"seed": 68695900,
"simplified_expr": "( (( 9 * 10)) * 7)",
"solutions_count": null,
"symbol_definitions": {
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"○": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是偶数",
"operation": " x - abs(y + x)"
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"default_operation": " x * y",
"precedence": 2
},
"◎": null,
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},
"target": null,
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"trace_id": "bb70e23a-245b-4b7e-a62b-dfff5d61f090"
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"question": "Define ○, the rules are as follows:\nwhen the sum of x and y is even, x ○ y = x - abs(y + x);\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: 9 ○ 10 ○ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 10 ○ 7",
"fill_length": null,
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"is_solvable": null,
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"numbers": null,
"operators": null,
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"seed": 68695900,
"simplified_expr": "( (( 9 * 10)) * 7)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是偶数",
"operation": " x - abs(y + x)"
}
],
"default_operation": " x * y",
"precedence": 2
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"trace_id": "bb70e23a-245b-4b7e-a62b-dfff5d61f090"
},
"seed": 68695900,
"task_id": 268695900,
"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
when y is a multiple of 5, x ◎ y = x * y ** x;
otherwise, x ◎ y = x + y - y.
and ⊕, the rules are as follows:
when x is equal to y, x ⊕ y = x ◎ y * 3;
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: 5 ⊕ 8
Please fill your final answer in \boxed{}. | {
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"gpt_response": "",
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"symbol_definitions": {
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"⊗": null,
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "y是5的倍数",
"operation": " x * y ** x"
}
],
"default_operation": " x + y - y",
"precedence": 3
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "c8ad1015-6681-4924-95ff-6afdc91b700e"
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"question": "Define ◎, the rules are as follows:\nwhen y is a multiple of 5, x ◎ y = x * y ** x;\notherwise, x ◎ y = x + y - y.\nand ⊕, the rules are as follows:\nwhen x is equal to y, x ⊕ y = x ◎ y * 3;\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: 5 ⊕ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 10356393,
"simplified_expr": "( 8 + 5 * 5)",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
"associativity": "left",
"conditions": [
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"⊗": null,
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"▽": null,
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"◎": {
"associativity": "left",
"conditions": [
{
"condition": "y是5的倍数",
"operation": " x * y ** x"
}
],
"default_operation": " x + y - y",
"precedence": 3
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "c8ad1015-6681-4924-95ff-6afdc91b700e"
},
"seed": 10356393,
"task_id": 210356393,
"task_type": "operation"
} |
logic-v2 | 定义 ○，规则如下：
当x是3的倍数时，x ○ y = y / y + x + 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10",
"fill_length": null,
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"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
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"seed": 75308592,
"simplified_expr": "10",
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"symbol_definitions": {
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"△": null,
"▽": null,
"◇": null,
"○": {
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"conditions": [
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"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "93426674-5031-489c-ad79-3667fe0d9153"
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"question": "定义 ○，规则如下：\n当x是3的倍数时，x ○ y = y / y + x + 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\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "10",
"fill_length": null,
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"solutions_count": null,
"symbol_definitions": {
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"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " y / y + x + x"
}
],
"default_operation": " (x - y - y) * x",
"precedence": 2
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"target": null,
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"trace_id": "93426674-5031-489c-ad79-3667fe0d9153"
},
"seed": 75308592,
"task_id": 275308592,
"task_type": "operation"
} |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * x + 2.
and ♡, the rules are as follows:
when x is a multiple of 3, x ♡ y = y + 4 * x;
otherwise, x ♡ y = y ⊕ x + x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x ⊕ y.
The precedence of operations: ♡ = ◎ > ** > * = / = % > + = - = ⊕。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ⊕ 5 ◎ 3 ♡ 7 ◎ 10
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "12440",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 5 ◎ 3 ♡ 7 ◎ 10",
"fill_length": 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": 78690272,
"simplified_expr": "( ((( 10 * ((((((((((3 * 5)) + 2)) * 7)) + 2)) + ((((3 * 5)) + 2)))) + 2))) * 9 + 2)",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
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"precedence": 1
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " x ⊕ y",
"precedence": 4
},
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " y + 4 * x"
}
],
"default_operation": " y ⊕ x + x",
"precedence": 4
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "e1c51497-5db6-4834-be2f-e1f7d10149c6"
},
"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = y * x + 2.\nand ♡, the rules are as follows:\nwhen x is a multiple of 3, x ♡ y = y + 4 * x;\notherwise, x ♡ y = y ⊕ x + x.\nand ◎, the rules are as follows:\non the real number field, x ◎ y = x ⊕ y.\nThe precedence of operations: ♡ = ◎ > ** > * = / = % > + = - = ⊕。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 ⊕ 5 ◎ 3 ♡ 7 ◎ 10\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 5 ◎ 3 ♡ 7 ◎ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
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"♡": {
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} |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y ** x - x + y + x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 1 / 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 less than y, x ☆ y = y + x - y - y + x;
otherwise, x ☆ y = y * y ** x / y - y.
and ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = x + y * y - y ☆ y;
otherwise, x ⊗ y = 1 + y * 3 / 5 ☆ x.
and ⊙, the rules are as follows:
when y is odd, x ⊙ y = y ⊗ 1 * 4 - 2 * x;
otherwise, x ⊙ y = 3 - y + 2 - x * 1.
The precedence of operations: ** = ☆ > * = / = % = ⊙ > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ⊗ 5 ⊙ 2 ☆ 8
Please fill your final answer in \boxed{}. | {
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"precedence": 1
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"⊙": {
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"conditions": [
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"condition": "y是奇数",
"operation": " y ⊗ 1 * 4 - 2 * x"
}
],
"default_operation": " 3 - y + 2 - x * 1",
"precedence": 2
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
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"condition": "x小于y",
"operation": " y + x - y - y + x"
}
],
"default_operation": " y * y ** x / y - y",
"precedence": 3
},
"♡": null,
"♢": null
},
"target": null,
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"question": "Define ☆, the rules are as follows:\nwhen x is less than y, x ☆ y = y + x - y - y + x;\notherwise, x ☆ y = y * y ** x / y - y.\nand ⊗, the rules are as follows:\nwhen x is greater than y, x ⊗ y = x + y * y - y ☆ y;\notherwise, x ⊗ y = 1 + y * 3 / 5 ☆ x.\nand ⊙, the rules are as follows:\nwhen y is odd, x ⊙ y = y ⊗ 1 * 4 - 2 * x;\notherwise, x ⊙ y = 3 - y + 2 - x * 1.\nThe precedence of operations: ** = ☆ > * = / = % = ⊙ > + = - = ⊗。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 8 ⊗ 5 ⊙ 2 ☆ 8\nPlease fill your final answer in \\boxed{}."
},
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"expression": "8 ⊗ 5 ⊙ 2 ☆ 8",
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"simplified_expr": "((((8 + ((((((((3 - ((((((((8 + 2)) - 8)) - 8)) + 2)))) + 2)) - ((5 * 1)))) * ((((((3 - ((((((((8 + 2)) - 8)) - 8)) + 2)))) + 2)) - ((5 * 1)))))))) - (( ((((((3 - ((((((((8 + 2)) - 8)) - 8)) + 2)))) + 2)) - ((5 * 1)))) * ((((((3 - ((((((((8 + 2)) - 8)) - 8)) + 2)))) + 2)) - ((5 * 1)))) ** ((((((3 - ((((((((8 + 2)) - 8)) - 8)) + 2)))) + 2)) - ((5 * 1)))) / ((((((3 - ((((((((8 + 2)) - 8)) - 8)) + 2)))) + 2)) - ((5 * 1)))) - ((((((3 - ((((((((8 + 2)) - 8)) - 8)) + 2)))) + 2)) - ((5 * 1))))))))",
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"operation": " x + y * y - y ☆ y"
}
],
"default_operation": " 1 + y * 3 / 5 ☆ x",
"precedence": 1
},
"⊙": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y ⊗ 1 * 4 - 2 * x"
}
],
"default_operation": " 3 - y + 2 - x * 1",
"precedence": 2
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
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"condition": "x小于y",
"operation": " y + x - y - y + x"
}
],
"default_operation": " y * y ** x / y - y",
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},
"♡": null,
"♢": null
},
"target": null,
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},
"seed": 45564504,
"task_id": 245564504,
"task_type": "operation"
} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y / (3 - x ** 3).
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: 3 ⊗ 7
Please fill your final answer in \boxed{}. | {
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"conditions": [],
"default_operation": " y / (3 - x ** 3)",
"precedence": 3
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"♡": null,
"♢": null
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = y / (3 - x ** 3).\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = y * (x + x).\nThe precedence of operations: ⊗ > ** = ☆ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ⊗ 7\nPlease fill your final answer in \\boxed{}."
},
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"solutions_count": null,
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
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} |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = x + y ** y。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10
请将最终答案填入\boxed{}中。 | {
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"answer": "10",
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"question": "定义 ▽，规则如下：\n实数域上，x ▽ y = x + y ** y。\n运算优先级：** = ▽ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * x + 4 + y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (y) / 5 * x / x.
and □, the rules are as follows:
on the real number field, x □ y = 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: 10 + 8 □ 9 ⊙ 6 ☆ 3
Please fill your final answer in \boxed{}. | {
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"○": null,
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"♢": null
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},
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"seed": 32965430,
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"task_type": "operation"
} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x / y.
and △, the rules are as follows:
on the real number field, x △ y = 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: 8 ♢ 7 △ 3 / 3 □ 3
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.\nand △, the rules are as follows:\non the real number field, x △ y = y * x + y.\nand □, the rules are as follows:\non the real number field, x □ y = x * x ♢ y.\nThe precedence of operations: ** = ♢ = △ = □ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 8 ♢ 7 △ 3 / 3 □ 3\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 ⊕，规则如下：
当x和y的和是偶数时，x ⊕ y = y - y / x + 5；
其他情况下，x ⊕ y = x - y - y - x。
和 ○，规则如下：
实数域上，x ○ y = x * x + y * y。
和 ☆，规则如下：
实数域上，x ☆ y = 2 / 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 ☆ 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊕，规则如下：\n当x和y的和是偶数时，x ⊕ y = y - y / x + 5；\n其他情况下，x ⊕ y = x - y - y - x。\n和 ○，规则如下：\n实数域上，x ○ y = x * x + y * y。\n和 ☆，规则如下：\n实数域上，x ☆ y = 2 / 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 ☆ 10\n请将最终答案填入\\boxed{}中。"
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logic-v2 | 定义 ⊕，规则如下：
当x和y都是奇数时，x ⊕ y = y + x；
其他情况下，x ⊕ y = x - x - y。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = x ⊕ x * y；
其他情况下，x ◎ y = x ⊕ 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: 3 ◎ 6 ▽ 1 ⊕ 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊕，规则如下：\n当x和y都是奇数时，x ⊕ y = y + x；\n其他情况下，x ⊕ y = x - x - y。\n和 ◎，规则如下：\n当x和y的和是奇数时，x ◎ y = x ⊕ x * y；\n其他情况下，x ◎ y = x ⊕ x + y。\n和 ▽，规则如下：\n实数域上，x ▽ y = y - y / x。\n运算优先级：** > * = / = % = ▽ > + = - = ⊕ = ◎。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 ◎ 6 ▽ 1 ⊕ 4\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 = 2 / x - x - y * x.
and ○, the rules are as follows:
when the sum of x and y is even, x ○ y = y / x ♢ y * y * y;
otherwise, x ○ y = x + (y) + x.
and ⊕, the rules are as follows:
when x is even, x ⊕ y = abs(x - y) + x;
otherwise, x ⊕ y = y - y + x * (x).
The precedence of operations: ○ = ⊕ > ** = ♢ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ♢ 8 ○ 8 ⊕ 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 = 2 / x - x - y * x.\nand ○, the rules are as follows:\nwhen the sum of x and y is even, x ○ y = y / x ♢ y * y * y;\notherwise, x ○ y = x + (y) + x.\nand ⊕, the rules are as follows:\nwhen x is even, x ⊕ y = abs(x - y) + x;\notherwise, x ⊕ y = y - y + x * (x).\nThe precedence of operations: ○ = ⊕ > ** = ♢ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 ♢ 8 ○ 8 ⊕ 2\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * x * x / x - y.
and ◇, the rules are as follows:
when y is odd, x ◇ y = x + x * y - y * x;
otherwise, x ◇ y = x * 3 + 2 - y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = (y - x * y) + 1.
The precedence of operations: ⊕ > ▽ > ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ▽ 9 ◇ 10 ⊕ 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 = y * x * x / x - y.\nand ◇, the rules are as follows:\nwhen y is odd, x ◇ y = x + x * y - y * x;\notherwise, x ◇ y = x * 3 + 2 - y.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = (y - x * y) + 1.\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 ◇ 10 ⊕ 5\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 ◇，规则如下：
当x和y都是奇数时，x ◇ y = x * x + y；
其他情况下，x ◇ y = x + (y * y)。
运算优先级：** = ◇ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ◇ 7 ◇ 8 - 8
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = 4 + y + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (x + y + x).
and ☆, the rules are as follows:
when y is odd, x ☆ y = x / x ♢ y;
otherwise, x ☆ y = x * x * y.
The precedence of operations: ♢ = ⊗ > ** > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ♢ 4 ☆ 6 ⊗ 8
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ♡，规则如下：
当y是奇数时，x ♡ y = y * 5 - x + (x) + x；
其他情况下，x ♡ y = x - y * 2 - 1 - y。
和 ○，规则如下：
当x是3的倍数时，x ○ y = x - abs(x / y + y)；
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: 8 ○ 8 ** 3 ♡ 5
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | 定义 ☆，规则如下：
当y是3的倍数时，x ☆ y = x + y - x * x * y；
其他情况下，x ☆ y = y * x * y - y / y。
和 ⊗，规则如下：
实数域上，x ⊗ y = y - 3 - x + y ☆ y。
运算优先级：⊗ > ☆ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ⊗ 10 * 1 ☆ 8
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ☆，规则如下：\n当y是3的倍数时，x ☆ y = x + y - x * x * y；\n其他情况下，x ☆ y = y * x * y - y / y。\n和 ⊗，规则如下：\n实数域上，x ⊗ y = y - 3 - x + y ☆ y。\n运算优先级：⊗ > ☆ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ⊗ 10 * 1 ☆ 8\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 = (x - y) - y * 3.
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 ⊗ 3 + 1 ○ 1 △ 8 % 6
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define ⊕, the rules are as follows:
when y is odd, x ⊕ y = y - x + y;
otherwise, x ⊕ y = (y * x).
and ◎, the rules are as follows:
on the real number field, x ◎ y = y + x + y * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y ⊕ x - x + x.
The precedence of operations: ⊕ > ◎ = ⊙ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ⊙ 4 ⊕ 3
Please fill your final answer in \boxed{}. | {
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logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = 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 □ 1
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是奇数时，x ♡ y = x * y + x / 4；
其他情况下，x ♡ y = y + x * x。
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: 4 ♡ 8 ☆ 4
请将最终答案填入\boxed{}中。 | {
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"seed": 53332674,
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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 = x ** y + y。
运算优先级：** = ♡ > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ♡ 8 △ 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ♡，规则如下：\n实数域上，x ♡ y = x / x * y。\n和 △，规则如下：\n实数域上，x △ y = x ** y + y。\n运算优先级：** = ♡ > * = / = % = △ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 ♡ 8 △ 4\n请将最终答案填入\\boxed{}中。"
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} |
logic-v2 | Define ⊕, the rules are as follows:
when y is a multiple of 3, x ⊕ y = abs(x ** x) - x - y * y;
otherwise, x ⊕ y = x - (x) - y / x.
and ☆, the rules are as follows:
when y is odd, x ☆ y = y ⊕ (y - 4) + x;
otherwise, x ☆ y = 1 + x + y - 3 * 1.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y * y * x - 3 ☆ y.
The precedence of operations: ▽ > ** > * = / = % > + = - = ⊕ = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ▽ 10 ☆ 9
Please fill your final answer in \boxed{}. | {
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"question": "Define ⊕, the rules are as follows:\nwhen y is a multiple of 3, x ⊕ y = abs(x ** x) - x - y * y;\notherwise, x ⊕ y = x - (x) - y / x.\nand ☆, the rules are as follows:\nwhen y is odd, x ☆ y = y ⊕ (y - 4) + x;\notherwise, x ☆ y = 1 + x + y - 3 * 1.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = y * y * x - 3 ☆ y.\nThe precedence of operations: ▽ > ** > * = / = % > + = - = ⊕ = ☆。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ▽ 10 ☆ 9\nPlease fill your final answer in \\boxed{}."
},
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},
"⊗": null,
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"▽": {
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"default_operation": " y * y * x - 3 ☆ y",
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},
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"○": null,
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"☆": {
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"conditions": [
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}
],
"default_operation": " 1 + x + y - 3 * 1",
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},
"♡": null,
"♢": null
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} |
logic-v2 | Define ◎, the rules are as follows:
when x is odd, x ◎ y = x * x + y - y;
otherwise, x ◎ y = (y + x) + 5 - x.
and □, the rules are as follows:
on the real number field, x □ y = x - y + 3 - x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y - x + y □ y.
The precedence of operations: □ > ** = ♡ > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ♡ 5 ◎ 2
Please fill your final answer in \boxed{}. | {
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"precedence": 2
},
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x + y □ y",
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},
"♢": null
},
"target": null,
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"question": "Define ◎, the rules are as follows:\nwhen x is odd, x ◎ y = x * x + y - y;\notherwise, x ◎ y = (y + x) + 5 - x.\nand □, the rules are as follows:\non the real number field, x □ y = x - y + 3 - x.\nand ♡, the rules are as follows:\non the real number field, x ♡ y = y - x + y □ y.\nThe precedence of operations: □ > ** = ♡ > * = / = % = ◎ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ♡ 5 ◎ 2\nPlease fill your final answer in \\boxed{}."
},
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"expression": "7 ♡ 5 ◎ 2",
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"solutions_count": null,
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"▽": null,
"◇": null,
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"operation": " x * x + y - y"
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},
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"♡": {
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"conditions": [],
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},
"♢": null
},
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},
"seed": 9654800,
"task_id": 209654800,
"task_type": "operation"
} |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = y + y ** 2 - x。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
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"gpt_response": "",
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"question": "定义 ◇，规则如下：\n实数域上，x ◇ y = y + y ** 2 - x。\n运算优先级：◇ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3\n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:
when x is odd, x ▽ y = 2 - y / x + y * 1;
otherwise, x ▽ y = 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: 9 ▽ 8
Please fill your final answer in \boxed{}. | {
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"question": "Define ▽, the rules are as follows:\nwhen x is odd, x ▽ y = 2 - y / x + y * 1;\notherwise, x ▽ y = y * (x / y + 4) - 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 ▽ 8\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define □, the rules are as follows:
when y is a multiple of 3, x □ y = x + y;
otherwise, x □ y = 3 + y + x.
The precedence of operations: □ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 □ 9 / 3
Please fill your final answer in \boxed{}. | {
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},
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"expression": "6 □ 9 / 3",
"fill_length": null,
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"operation": " x + y"
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logic-v2 | Define ▽, the rules are as follows:
when x and y are both even, x ▽ y = x * y + x;
otherwise, x ▽ y = x + x ** y.
and ◎, the rules are as follows:
when y is even, x ◎ y = x + y * x;
otherwise, x ◎ y = y * x + x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x - y * x.
The precedence of operations: ◎ > ** = ◇ > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ◇ 8 ◎ 1 ▽ 6
Please fill your final answer in \boxed{}. | {
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},
"○": null,
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"associativity": "left",
"conditions": [
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"condition": "y是偶数",
"operation": " x + y * x"
}
],
"default_operation": " y * x + x",
"precedence": 4
},
"☆": null,
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},
"target": null,
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"question": "Define ▽, the rules are as follows:\nwhen x and y are both even, x ▽ y = x * y + x;\notherwise, x ▽ y = x + x ** y.\nand ◎, the rules are as follows:\nwhen y is even, x ◎ y = x + y * x;\notherwise, x ◎ y = y * x + x.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = x - y * x.\nThe precedence of operations: ◎ > ** = ◇ > * = / = % > + = - = ▽。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 8 ◇ 8 ◎ 1 ▽ 6\nPlease fill your final answer in \\boxed{}."
},
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"expression": "8 ◇ 8 ◎ 1 ▽ 6",
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"seed": 3731890,
"simplified_expr": "( (( 8 - (( 1 * 8 + 8)) * 8)) * 6 + (( 8 - (( 1 * 8 + 8)) * 8)))",
"solutions_count": null,
"symbol_definitions": {
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"▽": {
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"operation": " x * y + x"
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},
"◇": {
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"conditions": [],
"default_operation": " x - y * x",
"precedence": 3
},
"○": null,
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "y是偶数",
"operation": " x + y * x"
}
],
"default_operation": " y * x + x",
"precedence": 4
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "22224dbd-29f4-4d50-bd19-27a881eca7ce"
},
"seed": 3731890,
"task_id": 203731890,
"task_type": "operation"
} |
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:
when the sum of x and y is even, x ○ y = x ♡ y;
otherwise, x ○ y = y * x - y + x.
The precedence of operations: ○ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ♡ 2
Please fill your final answer in \boxed{}. | {
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"conditions": [],
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"♢": null
},
"target": null,
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"trace_id": "1bf643e7-3204-4864-9514-caf91330ce98"
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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:\nwhen the sum of x and y is even, x ○ y = x ♡ y;\notherwise, x ○ y = y * x - y + x.\nThe precedence of operations: ○ > ** = ♡ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ♡ 2\nPlease fill your final answer in \\boxed{}."
},
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"expression": "5 ♡ 2",
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"operators": null,
"question_sequence": null,
"seed": 18965484,
"simplified_expr": "( (2 - 5) - 2 + 2)",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
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"□": null,
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"▽": null,
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"○": {
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"operation": " x ♡ y"
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},
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"seed": 18965484,
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} |
logic-v2 | 定义 ⊙，规则如下：
当x是3的倍数时，x ⊙ y = y * x + y；
其他情况下，x ⊙ y = (x + y + y + x)。
和 ▽，规则如下：
实数域上，x ▽ y = abs(x - 5 - y / x)。
和 ♢，规则如下：
实数域上，x ♢ y = y * x * y。
运算优先级：▽ > ** = ⊙ = ♢ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ♢ 9 ♢ 2 ▽ 9 ⊙ 8
请将最终答案填入\boxed{}中。 | {
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},
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}
},
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"trace_id": "d6f47770-480c-402c-9e33-b9f461f732ef"
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"question": "定义 ⊙，规则如下：\n当x是3的倍数时，x ⊙ y = y * x + y；\n其他情况下，x ⊙ y = (x + y + y + x)。\n和 ▽，规则如下：\n实数域上，x ▽ y = abs(x - 5 - y / x)。\n和 ♢，规则如下：\n实数域上，x ♢ y = y * x * y。\n运算优先级：▽ > ** = ⊙ = ♢ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 7 ♢ 9 ♢ 2 ▽ 9 ⊙ 8\n请将最终答案填入\\boxed{}中。"
},
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},
"◇": null,
"○": null,
"◎": null,
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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 = x - y ⊕ x.
and △, the rules are as follows:
on the real number field, x △ y = x + y * y.
The precedence of operations: ⊕ = ⊙ > ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 △ 5 △ 4 ⊙ 8 ⊕ 5
Please fill your final answer in \boxed{}. | {
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"conditions": [],
"default_operation": " x - y ⊕ x",
"precedence": 5
},
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"associativity": "left",
"conditions": [],
"default_operation": " x + y * y",
"precedence": 2
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "c6cbb3de-c787-4537-b7bc-474fa2f8a89d"
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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 = x - y ⊕ x.\nand △, the rules are as follows:\non the real number field, x △ y = x + y * y.\nThe precedence of operations: ⊕ = ⊙ > ** > * = / = % = △ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 △ 5 △ 4 ⊙ 8 ⊕ 5\nPlease fill your final answer in \\boxed{}."
},
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"seed": 28861410,
"simplified_expr": "( (( 9 + 5 * 5)) + (( (((4 - (( 8 - 4 * 4))))) - 5 * 5)) * (( (((4 - (( 8 - 4 * 4))))) - 5 * 5)))",
"solutions_count": null,
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"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y ⊕ x",
"precedence": 5
},
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"△": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y * y",
"precedence": 2
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"seed": 28861410,
"task_id": 228861410,
"task_type": "operation"
} |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y * x - 4。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 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 = y * x - 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: 3 △ 10\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | Define ◇, the rules are as follows:
when x is odd, x ◇ y = x * y + y * x;
otherwise, x ◇ y = x - y * x * x - y.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ♢，规则如下：
当x小于y时，x ♢ y = abs(y + x)；
其他情况下，x ♢ y = y - x * x。
和 ⊗，规则如下：
实数域上，x ⊗ y = y ♢ y / x。
和 ⊕，规则如下：
实数域上，x ⊕ y = y - 4 ♢ x。
运算优先级：♢ > ** > * = / = % = ⊗ > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊕ 8 ⊕ 8 ♢ 6 ⊗ 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ♢，规则如下：\n当x小于y时，x ♢ y = abs(y + x)；\n其他情况下，x ♢ y = y - x * x。\n和 ⊗，规则如下：\n实数域上，x ⊗ y = y ♢ y / x。\n和 ⊕，规则如下：\n实数域上，x ⊕ y = y - 4 ♢ x。\n运算优先级：♢ > ** > * = / = % = ⊗ > + = - = ⊕。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 ⊕ 8 ⊕ 8 ♢ 6 ⊗ 4\n请将最终答案填入\\boxed{}中。"
},
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} |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = y + x * (x - x)。
和 □，规则如下：
当x小于y时，x □ y = y * x - (y - y * 2)；
其他情况下，x □ y = 4 + 1 ♡ 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: 1 □ 4 ♡ 9 ** 1
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ♡，规则如下：\n实数域上，x ♡ y = y + x * (x - x)。\n和 □，规则如下：\n当x小于y时，x □ y = y * x - (y - y * 2)；\n其他情况下，x □ y = 4 + 1 ♡ 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: 1 □ 4 ♡ 9 ** 1\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3的倍数时，x ☆ y = x + 3 + y - x + 4；
其他情况下，x ☆ y = (x) + x * 1 - y。
和 □，规则如下：
当x和y都是奇数时，x □ y = 4 - 5 ☆ y * 2 / x；
其他情况下，x □ y = 2 * y ☆ x + 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: 5 * 9 □ 10 ☆ 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是3的倍数时，x □ y = y - 5 * x；
其他情况下，x □ y = y + x + x + x。
和 ☆，规则如下：
当x和y的和是奇数时，x ☆ y = y □ y * x；
其他情况下，x ☆ y = y □ 5 * 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 ☆ 10 □ 8
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = 5 + x + y * y - x.
and △, the rules are as follows:
when x and y are both even, x △ y = y - x + y - x * 3;
otherwise, x △ y = 5 ☆ y * x + 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: 5 △ 3
Please fill your final answer in \boxed{}. | {
"game_data": {
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"simplified_expr": "(((((( 5 + 5 + 3 * 3 - 5)) * 5)) + 5))",
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"◎": null,
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"♡": null,
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = 5 + x + y * y - x.\nand △, the rules are as follows:\nwhen x and y are both even, x △ y = y - x + y - x * 3;\notherwise, x △ y = 5 ☆ y * x + 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: 5 △ 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "5 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 11675940,
"simplified_expr": "(((((( 5 + 5 + 3 * 3 - 5)) * 5)) + 5))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " y - x + y - x * 3"
}
],
"default_operation": " 5 ☆ y * x + 5",
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},
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"○": null,
"◎": null,
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},
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "55f0344a-ee08-4076-9c55-3f85cf73d99b"
},
"seed": 11675940,
"task_id": 211675940,
"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: 4 ○ 10 % 6
Please fill your final answer in \boxed{}. | {
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"answer": "2.4",
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"gpt_response": "",
"metadata": {
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"expression": "4 ○ 10 % 6",
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"seed": 75498545,
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"solutions_count": null,
"symbol_definitions": {
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"▽": null,
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"○": {
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},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "7a5521bb-d80e-4c7b-af9c-e84fbda7e858"
},
"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: 4 ○ 10 % 6\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 10 % 6",
"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": 75498545,
"simplified_expr": "((( 4 + 4 / 10 + 10)) % 6)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x + x / y + y",
"precedence": 3
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "7a5521bb-d80e-4c7b-af9c-e84fbda7e858"
},
"seed": 75498545,
"task_id": 275498545,
"task_type": "operation"
} |
logic-v2 | Define ♢, the rules are as follows:
when x is a multiple of 5, x ♢ y = (y + 3 * 1 * x);
otherwise, x ♢ y = 5 * 1 * y - x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y / x * y * 4.
and ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = x + (y + x * y) ♢ x;
otherwise, x ⊙ y = x ♢ y * y * y - y.
The precedence of operations: ** > * = / = % = ◎ = ⊙ > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ♢ 6 ⊙ 4
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "325",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 6 ⊙ 4",
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"seed": 83188106,
"simplified_expr": "( (((((( 5 * 1 * ((((4 * 4)) * 4)) - 6)) - 4))) + 3 * 1 * 5))",
"solutions_count": null,
"symbol_definitions": {
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"operation": " x + (y + x * y) ♢ x"
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"precedence": 2
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x * y * 4",
"precedence": 2
},
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是5的倍数",
"operation": " (y + 3 * 1 * x)"
}
],
"default_operation": " 5 * 1 * y - x",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "e0e92036-b6b1-419e-bdea-49e03cc06347"
},
"question": "Define ♢, the rules are as follows:\nwhen x is a multiple of 5, x ♢ y = (y + 3 * 1 * x);\notherwise, x ♢ y = 5 * 1 * y - x.\nand ◎, the rules are as follows:\non the real number field, x ◎ y = y / x * y * 4.\nand ⊙, the rules are as follows:\nwhen the sum of x and y is odd, x ⊙ y = x + (y + x * y) ♢ x;\notherwise, x ⊙ y = x ♢ y * y * y - y.\nThe precedence of operations: ** > * = / = % = ◎ = ⊙ > + = - = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ♢ 6 ⊙ 4\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "5 ♢ 6 ⊙ 4",
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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": 83188106,
"simplified_expr": "( (((((( 5 * 1 * ((((4 * 4)) * 4)) - 6)) - 4))) + 3 * 1 * 5))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是奇数",
"operation": " x + (y + x * y) ♢ x"
}
],
"default_operation": " x ♢ y * y * y - y",
"precedence": 2
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x * y * 4",
"precedence": 2
},
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是5的倍数",
"operation": " (y + 3 * 1 * x)"
}
],
"default_operation": " 5 * 1 * y - x",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "e0e92036-b6b1-419e-bdea-49e03cc06347"
},
"seed": 83188106,
"task_id": 283188106,
"task_type": "operation"
} |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + x + y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * 1 + y.
and ○, the rules are as follows:
on the real number field, x ○ y = x * y + y.
The precedence of operations: ** = ⊗ > * = / = % = ○ > + = - = ⊕。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ○ 8 ⊗ 5 ⊕ 6
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"expression": "4 ○ 8 ⊗ 5 ⊕ 6",
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"n_types": null,
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"seed": 75192336,
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"solutions_count": null,
"symbol_definitions": {
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"conditions": [],
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},
"⊗": {
"associativity": "left",
"conditions": [],
"default_operation": " x + x + y",
"precedence": 3
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y + y",
"precedence": 2
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "6a6d057c-6c27-4ed7-927e-3067003cfc52"
},
"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = x + x + y.\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = x * 1 + y.\nand ○, the rules are as follows:\non the real number field, x ○ y = x * y + y.\nThe precedence of operations: ** = ⊗ > * = / = % = ○ > + = - = ⊕。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ○ 8 ⊗ 5 ⊕ 6\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 8 ⊗ 5 ⊕ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 75192336,
"simplified_expr": "( (( 4 * (( 8 + 8 + 5)) + (( 8 + 8 + 5)))) * 1 + 6)",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
"associativity": "left",
"conditions": [],
"default_operation": " x * 1 + y",
"precedence": 1
},
"⊗": {
"associativity": "left",
"conditions": [],
"default_operation": " x + x + y",
"precedence": 3
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y + y",
"precedence": 2
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "6a6d057c-6c27-4ed7-927e-3067003cfc52"
},
"seed": 75192336,
"task_id": 275192336,
"task_type": "operation"
} |
logic-v2 | Define □, the rules are as follows:
when x is even, x □ y = y * abs(3 - x * x);
otherwise, x □ y = x * y + 3 * x.
and ○, the rules are as follows:
when x is a multiple of 5, x ○ y = (x * y) □ y * 4;
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: 1 ○ 8 % 4 □ 4
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "2",
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"gpt_response": "",
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"expression": "1 ○ 8 % 4 □ 4",
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"n_types": null,
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"num_of_numbers": null,
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 85217483,
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"solutions_count": null,
"symbol_definitions": {
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],
"default_operation": " x * y + 3 * x",
"precedence": 4
},
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x是5的倍数",
"operation": " (x * y) □ y * 4"
}
],
"default_operation": " x * x + y / y",
"precedence": 4
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "09bdc42f-cef2-40eb-9684-e8ba5a86dbee"
},
"question": "Define □, the rules are as follows:\nwhen x is even, x □ y = y * abs(3 - x * x);\notherwise, x □ y = x * y + 3 * x.\nand ○, the rules are as follows:\nwhen x is a multiple of 5, x ○ y = (x * y) □ y * 4;\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: 1 ○ 8 % 4 □ 4\nPlease fill your final answer in \\boxed{}."
},
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"expression": "1 ○ 8 % 4 □ 4",
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"num_of_numbers": null,
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"numbers": null,
"operators": null,
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"seed": 85217483,
"simplified_expr": "((( 1 * 1 + 8 / 8)) % (( 4 * abs(3 - 4 * 4))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " y * abs(3 - x * x)"
}
],
"default_operation": " x * y + 3 * x",
"precedence": 4
},
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x是5的倍数",
"operation": " (x * y) □ y * 4"
}
],
"default_operation": " x * x + y / y",
"precedence": 4
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "09bdc42f-cef2-40eb-9684-e8ba5a86dbee"
},
"seed": 85217483,
"task_id": 285217483,
"task_type": "operation"
} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x * y - y + y.
and ⊗, the rules are as follows:
on the real number field, 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: 5 ⊗ 7
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "31",
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"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 7",
"fill_length": 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": 81951285,
"simplified_expr": "( (1 + 7 * 5) - 5)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [],
"default_operation": " (1 + y * x) - x",
"precedence": 2
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y - y + y",
"precedence": 2
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "8f711b79-3bab-404e-9711-b6e8c54fd22c"
},
"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = x * y - y + y.\nand ⊗, the rules are as follows:\non the real number field, 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: 5 ⊗ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 81951285,
"simplified_expr": "( (1 + 7 * 5) - 5)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [],
"default_operation": " (1 + y * x) - x",
"precedence": 2
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y - y + y",
"precedence": 2
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "8f711b79-3bab-404e-9711-b6e8c54fd22c"
},
"seed": 81951285,
"task_id": 281951285,
"task_type": "operation"
} |
logic-v2 | Define ♡, the rules are as follows:
when x is less than y, x ♡ y = x + y ** y - y;
otherwise, x ♡ y = x * (y).
and □, the rules are as follows:
when x is odd, x □ y = y + y - x;
otherwise, x □ y = x * x + x * y.
and ○, the rules are as follows:
when x is equal to y, x ○ y = x / y + x ♡ y;
otherwise, x ○ y = 4 + x * y - y.
The precedence of operations: □ > ** > * = / = % = ♡ = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 □ 8 ♡ 8
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ◇，规则如下：
当x等于y时，x ◇ y = 2 - 2 + (1 ** x) / y；
其他情况下，x ◇ y = y * y + x + 1。
和 ⊗，规则如下：
当x和y的和是奇数时，x ⊗ y = x + 3 * 1 ◇ y；
其他情况下，x ⊗ y = x ◇ 2 - 4 + y。
和 ⊕，规则如下：
实数域上，x ⊕ y = 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: 8 ⊗ 3 ◇ 7 ⊕ 2
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y * x。
和 ◇，规则如下：
实数域上，x ◇ 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 ⊕ 4 ◇ 5
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊕，规则如下：\n实数域上，x ⊕ y = y * x。\n和 ◇，规则如下：\n实数域上，x ◇ y = x ⊕ y。\n和 ♢，规则如下：\n实数域上，x ♢ y = (y * x ** x)。\n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 ⊕ 4 ◇ 5\n请将最终答案填入\\boxed{}中。"
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logic-v2 | 定义 ⊙，规则如下：
当x和y都是奇数时，x ⊙ y = abs(y) * y + x；
其他情况下，x ⊙ y = y * y / x - y。
和 ♢，规则如下：
实数域上，x ♢ y = x * y ** 1 * x。
和 ♡，规则如下：
当x是奇数时，x ♡ y = 4 ** 3 ⊙ y + x；
其他情况下，x ♡ y = 5 + y + x。
运算优先级：⊙ > ♢ = ♡ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊙ 2 ♡ 7 ♢ 6
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x * abs(y)。
和 ◇，规则如下：
当x等于y时，x ◇ y = x * x ◎ y * y * y；
其他情况下，x ◇ y = 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 ◇ 3 - 5 ◎ 9
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ⊗，规则如下：
当y是3的倍数时，x ⊗ y = 4 ** y ** x * y + y；
其他情况下，x ⊗ y = y + x * y * x - x。
和 △，规则如下：
实数域上，x △ y = abs(5 / x ** 3) - y。
和 □，规则如下：
当x等于y时，x □ y = (1 - 3 * 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: 9 □ 8 △ 9 ⊗ 2
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊗，规则如下：\n当y是3的倍数时，x ⊗ y = 4 ** y ** x * y + y；\n其他情况下，x ⊗ y = y + x * y * x - x。\n和 △，规则如下：\n实数域上，x △ y = abs(5 / x ** 3) - y。\n和 □，规则如下：\n当x等于y时，x □ y = (1 - 3 * 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: 9 □ 8 △ 9 ⊗ 2\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 = abs(y + x + y - x - x).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y - 3 * 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: 9 ▽ 9
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: 8 △ 8
Please fill your final answer in \boxed{}. | {
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"question": "Define △, the rules are as follows:\non the real number field, x △ y = y + y - 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 △ 8\nPlease fill your final answer in \\boxed{}."
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logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x - x + y * y + x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = (x - 4 ♢ 2) + y * y.
and ◎, the rules are as follows:
when x is equal to y, x ◎ y = 2 * y * x + x - y;
otherwise, x ◎ y = x + y - x - 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 ⊙ 8 ♢ 4 ◎ 7
Please fill your final answer in \boxed{}. | {
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"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = x - x + y * y + x.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = (x - 4 ♢ 2) + y * y.\nand ◎, the rules are as follows:\nwhen x is equal to y, x ◎ y = 2 * y * x + x - y;\notherwise, x ◎ y = x + y - x - 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 ⊙ 8 ♢ 4 ◎ 7\nPlease fill your final answer in \\boxed{}."
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logic-v2 | Define ○, the rules are as follows:
when the sum of x and y is even, x ○ y = y + x;
otherwise, x ○ y = abs(y * y + x).
and ☆, the rules are as follows:
when the sum of x and y is even, x ☆ y = 4 * x / y / 2;
otherwise, x ☆ y = (y * 3) + x.
The precedence of operations: ○ > ** > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ☆ 9
Please fill your final answer in \boxed{}. | {
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"precedence": 1
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"conditions": [
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"operation": " 4 * x / y / 2"
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"precedence": 1
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logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y - x - abs(y).
and ◇, the rules are as follows:
on the real number field, x ◇ y = y + x - 1.
The precedence of operations: ◎ > ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ◎ 6 ◎ 4 * 7 ◇ 4
Please fill your final answer in \boxed{}. | {
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = y - x - abs(y).\nand ◇, the rules are as follows:\non the real number field, x ◇ y = y + x - 1.\nThe precedence of operations: ◎ > ** > * = / = % > + = - = ◇。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 ◎ 6 ◎ 4 * 7 ◇ 4\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 △，规则如下：
当x小于y时，x △ y = x + y / y - 5；
其他情况下，x △ y = abs(5 * 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: 5 △ 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 = 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: 6 △ 2
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 - 3。
和 △，规则如下：
实数域上，x △ y = y * x + 5 ⊗ x。
和 ♡，规则如下：
实数域上，x ♡ y = (x - x + x) * y / y。
运算优先级：△ > ** > * = / = % = ⊗ = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊗ 3 ♡ 5 ⊗ 4 △ 8
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 * 3 - x - y。
和 ⊗，规则如下：
当x是奇数时，x ⊗ y = y * y - x - 3 * x；
其他情况下，x ⊗ y = y - x - x。
运算优先级：** > * = / = % = ♡ = ⊗ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊗ 10
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y + x / 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: 3 ◇ 6 + 4 ◇ 2
Please fill your final answer in \boxed{}. | {
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logic-v2 | Define □, the rules are as follows:
when x is greater than y, x □ y = y + 4 / x;
otherwise, x □ y = y - x ** x.
and ⊙, the rules are as follows:
when y is a multiple of 5, x ⊙ y = x / y;
otherwise, x ⊙ y = (y / x) / x.
The precedence of operations: ⊙ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ⊙ 10 □ 7
Please fill your final answer in \boxed{}. | {
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logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + 5 * y.
and □, the rules are as follows:
on the real number field, x □ y = y + x * abs(y).
and ◎, the rules are as follows:
when x is less than y, x ◎ y = (4 ** x □ y);
otherwise, x ◎ y = (x + y) / 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: 7 ◎ 5 ⊗ 9
Please fill your final answer in \boxed{}. | {
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"◎": {
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"conditions": [
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"condition": "x小于y",
"operation": " (4 ** x □ y)"
}
],
"default_operation": " (x + y) / 4",
"precedence": 4
},
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"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = x + 5 * y.\nand □, the rules are as follows:\non the real number field, x □ y = y + x * abs(y).\nand ◎, the rules are as follows:\nwhen x is less than y, x ◎ y = (4 ** x □ y);\notherwise, x ◎ y = (x + y) / 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: 7 ◎ 5 ⊗ 9\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 ⊕，规则如下：
当x和y的和是偶数时，x ⊕ y = y + x + x；
其他情况下，x ⊕ y = x / y。
和 ○，规则如下：
实数域上，x ○ y = y ⊕ (x ** y)。
和 ♡，规则如下：
当x大于y时，x ♡ y = y + x；
其他情况下，x ♡ y = x + 5 + y。
运算优先级：⊕ = ○ > ** = ♡ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 4 ○ 4 ⊕ 5
请将最终答案填入\boxed{}中。 | {
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"operation": " y + x"
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"question": "定义 ⊕，规则如下：\n当x和y的和是偶数时，x ⊕ y = y + x + x；\n其他情况下，x ⊕ y = x / y。\n和 ○，规则如下：\n实数域上，x ○ y = y ⊕ (x ** y)。\n和 ♡，规则如下：\n当x大于y时，x ♡ y = y + x；\n其他情况下，x ♡ y = x + 5 + y。\n运算优先级：⊕ = ○ > ** = ♡ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 ♡ 4 ○ 4 ⊕ 5\n请将最终答案填入\\boxed{}中。"
},
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"conditions": [
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"operation": " y + x"
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"precedence": 3
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"seed": 24803471,
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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 is a multiple of 3, x ◎ y = x * y - x;
otherwise, x ◎ y = x ◇ y.
The precedence of operations: ◎ > ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ◎ 4 ◇ 1 + 9
Please fill your final answer in \boxed{}. | {
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"question": "Define ◇, the rules are as follows:\non the real number field, x ◇ y = y + y - x.\nand ◎, the rules are as follows:\nwhen x is a multiple of 3, x ◎ y = x * y - x;\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: 4 ◎ 4 ◇ 1 + 9\nPlease fill your final answer in \\boxed{}."
},
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"seed": 21517860,
"simplified_expr": "((( 1 + 1 - ((( 4 + 4 - 4))))) + 9)",
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"operation": " x * y - x"
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"seed": 21517860,
"task_id": 221517860,
"task_type": "operation"
} |
logic-v2 | Define ○, 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: 8 / 9 ○ 1 * 3
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 * 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 / 9 ○ 1 * 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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} |
logic-v2 | 定义 ◇，规则如下：
当y是偶数时，x ◇ y = 1 - y - x + 2 - x；
其他情况下，x ◇ y = y + (x + y - y ** y)。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1
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 y is a multiple of 3, x ♡ y = 1 - (x / y / x);
otherwise, x ♡ y = y - y + x.
and □, the rules are as follows:
when y is a multiple of 3, x □ y = (x ** y);
otherwise, x □ 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: 2 □ 6 ♡ 7
Please fill your final answer in \boxed{}. | {
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "y是3的倍数",
"operation": " 1 - (x / y / x)"
}
],
"default_operation": " y - y + x",
"precedence": 4
},
"♢": null
},
"target": null,
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"question": "Define ♡, the rules are as follows:\nwhen y is a multiple of 3, x ♡ y = 1 - (x / y / x);\notherwise, x ♡ y = y - y + x.\nand □, the rules are as follows:\nwhen y is a multiple of 3, x □ y = (x ** y);\notherwise, x □ y = abs(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 □ 6 ♡ 7\nPlease fill your final answer in \\boxed{}."
},
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"▽": null,
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"○": null,
"◎": null,
"☆": null,
"♡": {
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"conditions": [
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"condition": "y是3的倍数",
"operation": " 1 - (x / y / x)"
}
],
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"precedence": 4
},
"♢": null
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"seed": 22082631,
"task_id": 222082631,
"task_type": "operation"
} |
logic-v2 | Define ⊕, the rules are as follows:
when x is odd, x ⊕ y = 3 - x / y;
otherwise, x ⊕ y = x - x + y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - x * x.
and △, the rules are as follows:
when x is odd, x △ y = (x) ⊙ 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: 1 ⊕ 8 △ 5 ⊙ 1
Please fill your final answer in \boxed{}. | {
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"operation": " (x) ⊙ y"
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},
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"question": "Define ⊕, the rules are as follows:\nwhen x is odd, x ⊕ y = 3 - x / y;\notherwise, x ⊕ y = x - x + y.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = y - x * x.\nand △, the rules are as follows:\nwhen x is odd, x △ y = (x) ⊙ 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: 1 ⊕ 8 △ 5 ⊙ 1\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * y + 1 - y * (x).
and △, the rules are as follows:
on the real number field, x △ y = abs(x) ** y.
and ⊙, the rules are as follows:
when x is a multiple of 5, x ⊙ y = y △ x - x + x;
otherwise, x ⊙ y = x / y ⊕ 3 - x - x.
The precedence of operations: ⊙ > ⊕ = △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ⊙ 7 △ 5 ⊕ 2
Please fill your final answer in \boxed{}. | {
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},
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"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = y * y + 1 - y * (x).\nand △, the rules are as follows:\non the real number field, x △ y = abs(x) ** y.\nand ⊙, the rules are as follows:\nwhen x is a multiple of 5, x ⊙ y = y △ x - x + x;\notherwise, x ⊙ y = x / y ⊕ 3 - x - x.\nThe precedence of operations: ⊙ > ⊕ = △ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ⊙ 7 △ 5 ⊕ 2\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( 2 * 2 + 1 - 2 * ((( abs((((((((3 / (( 3 * 3 + 1 - 3 * (7))))) - 3)) - 3)))) ** 5))))",
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"precedence": 5
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"default_operation": " abs(x) ** y",
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},
"▽": null,
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"○": null,
"◎": null,
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logic-v2 | 定义 ◇，规则如下：
当x和y的和是奇数时，x ◇ y = 3 / x - y + x；
其他情况下，x ◇ y = x * x / 5 * y * x。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ◇ 1
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 = 3 / x - y + x；\n其他情况下，x ◇ y = x * x / 5 * y * x。\n运算优先级：◇ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 ◇ 1\n请将最终答案填入\\boxed{}中。"
},
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} |
logic-v2 | 定义 ♢，规则如下：
当x和y都是偶数时，x ♢ y = (x) / y；
其他情况下，x ♢ y = x - x * y。
和 △，规则如下：
实数域上，x △ y = x - x / y。
和 ☆，规则如下：
实数域上，x ☆ y = x + x - y。
运算优先级：△ > ** = ☆ > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ☆ 7 ☆ 7 △ 2 ♢ 8
请将最终答案填入\boxed{}中。 | {
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"conditions": [
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"operation": " (x) / y"
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"question": "定义 ♢，规则如下：\n当x和y都是偶数时，x ♢ y = (x) / y；\n其他情况下，x ♢ y = x - x * y。\n和 △，规则如下：\n实数域上，x △ y = x - x / y。\n和 ☆，规则如下：\n实数域上，x ☆ y = x + 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: 9 ☆ 7 ☆ 7 △ 2 ♢ 8\n请将最终答案填入\\boxed{}中。"
},
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"simplified_expr": "( (( (( 9 + 9 - 7)) + (( 9 + 9 - 7)) - (( 7 - 7 / 2)))) - (( (( 9 + 9 - 7)) + (( 9 + 9 - 7)) - (( 7 - 7 / 2)))) * 8)",
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},
"▽": null,
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"○": null,
"◎": null,
"☆": {
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"conditions": [
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"operation": " (x) / y"
}
],
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logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x - (y * x - y).
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 △ 8
Please fill your final answer in \boxed{}. | {
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},
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"○": null,
"◎": null,
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logic-v2 | Define ▽, 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: 2 ▽ 6
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 * y - y ** x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = abs(x) + y.
The precedence of operations: ** > * = / = % = ◎ > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ◎ 5
Please fill your final answer in \boxed{}. | {
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}
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = y * y - y ** x.\nand ♢, the rules are as follows:\non the real number field, x ♢ y = abs(x) + y.\nThe precedence of operations: ** > * = / = % = ◎ > + = - = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ◎ 5\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define ♢, the rules are as follows:
when y is even, x ♢ y = 1 / x ** y;
otherwise, x ♢ y = x - y + x + 1.
and ⊕, the rules are as follows:
when x is equal to y, x ⊕ y = x - y - y;
otherwise, x ⊕ y = (x) - x + 2 - y.
and ⊙, the rules are as follows:
when x is odd, x ⊙ y = y ** x + y + x;
otherwise, x ⊙ y = y ** x + y ⊕ y.
The precedence of operations: ** = ⊕ > * = / = % = ⊙ > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ⊙ 2 ♢ 9
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define ⊕, the rules are as follows:
when x is less than y, x ⊕ y = x / y;
otherwise, x ⊕ y = 3 / x - y.
and ☆, the rules are as follows:
when x is less than y, x ☆ y = x ⊕ y * y;
otherwise, x ☆ y = y + x.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = y + x * x;
otherwise, x ♡ y = x + y - y.
The precedence of operations: ♡ > ** = ⊕ = ☆ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ☆ 6 ⊕ 4 ⊕ 2 ♡ 7
Please fill your final answer in \boxed{}. | {
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"operation": " y + x * x"
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"precedence": 4
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"♢": null
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"question": "Define ⊕, the rules are as follows:\nwhen x is less than y, x ⊕ y = x / y;\notherwise, x ⊕ y = 3 / x - y.\nand ☆, the rules are as follows:\nwhen x is less than y, x ☆ y = x ⊕ y * y;\notherwise, x ☆ y = y + x.\nand ♡, the rules are as follows:\nwhen the sum of x and y is odd, x ♡ y = y + x * x;\notherwise, x ♡ y = x + y - y.\nThe precedence of operations: ♡ > ** = ⊕ = ☆ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ☆ 6 ⊕ 4 ⊕ 2 ♡ 7\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 △，规则如下：
当x小于y时，x △ y = y * y * x + x - y；
其他情况下，x △ y = y * y - x - 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
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等于y时，x △ y = 5 * x * y；
其他情况下，x △ y = 5 - 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 △ 8
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 * x;
otherwise, x ○ y = 3 * y - x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = 1 ○ x - 3 + y.
and ◇, the rules are as follows:
when x is a multiple of 5, x ◇ y = 1 - y / y - x - x;
otherwise, x ◇ y = x ♢ (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: 1 ○ 6 ◇ 1 ♢ 8
Please fill your final answer in \boxed{}. | {
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"operation": " y + y - x + y * x"
}
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},
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}
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},
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},
"◎": null,
"☆": null,
"♡": null,
"♢": {
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"default_operation": " 1 ○ x - 3 + y",
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} |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = 2 - x * y。
和 ○，规则如下：
实数域上，x ○ y = 5 + y / 4 - x。
运算优先级：○ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ◎ 10 ○ 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 = 2 - x * y。\n和 ○，规则如下：\n实数域上，x ○ y = 5 + y / 4 - x。\n运算优先级：○ > ** > * = / = % > + = - = ◎。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 ◎ 10 ○ 4\n请将最终答案填入\\boxed{}中。"
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logic-v2 | 定义 ⊕，规则如下：
当x和y的和是偶数时，x ⊕ y = x + y + y；
其他情况下，x ⊕ y = x - y + x。
和 □，规则如下：
当x和y的和是奇数时，x □ y = (x + y + y)；
其他情况下，x □ y = y + y ⊕ x。
和 ⊗，规则如下：
实数域上，x ⊗ y = abs(y + x) * x。
运算优先级：□ > ** > * = / = % = ⊕ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ⊕ 1 □ 8 □ 5 ⊗ 6
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y - (y) - x。
和 ⊙，规则如下：
实数域上，x ⊙ y = x + y。
运算优先级：** > * = / = % = ☆ > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ☆ 10 ⊙ 6 ⊙ 4
请将最终答案填入\boxed{}中。 | {
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},
"metadata": {
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logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ 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: 6 * 3 ◇ 3 + 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◇，规则如下：\n实数域上，x ◇ y = x + 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 * 3 ◇ 3 + 4\n请将最终答案填入\\boxed{}中。"
},
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"◇": {
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logic-v2 | Define □, the rules are as follows:
when x is equal to y, x □ y = (y + x) - 4;
otherwise, x □ y = y - 4 + x + 2 - x.
and ♡, the rules are as follows:
when y is odd, x ♡ y = y - x / (x * x);
otherwise, x ♡ y = y - 5 - abs(1) * 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: 9 □ 4
Please fill your final answer in \boxed{}. | {
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"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
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"condition": "y是奇数",
"operation": " y - x / (x * x)"
}
],
"default_operation": " y - 5 - abs(1) * x * 4",
"precedence": 5
},
"♢": null
},
"target": null,
"total_length": null,
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"question": "Define □, the rules are as follows:\nwhen x is equal to y, x □ y = (y + x) - 4;\notherwise, x □ y = y - 4 + x + 2 - x.\nand ♡, the rules are as follows:\nwhen y is odd, x ♡ y = y - x / (x * x);\notherwise, x ♡ y = y - 5 - abs(1) * 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: 9 □ 4\nPlease fill your final answer in \\boxed{}."
},
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"expression": "9 □ 4",
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"operators": null,
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y - x / (x * x)"
}
],
"default_operation": " y - 5 - abs(1) * x * 4",
"precedence": 5
},
"♢": null
},
"target": null,
"total_length": null,
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},
"seed": 60760914,
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"task_type": "operation"
} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = (y) * 3 + x.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = x - x * y;
otherwise, x ♡ y = 4 - x + x * y.
and ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = x + y * x;
otherwise, x ▽ y = x + y.
The precedence of operations: ▽ > ** > * = / = % > + = - = ♢ = ♡。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ♢ 8 ▽ 2
Please fill your final answer in \boxed{}. | {
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"○": null,
"◎": null,
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"conditions": [
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"condition": "x和y的和是奇数",
"operation": " x - x * y"
}
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"default_operation": " 4 - x + x * y",
"precedence": 1
},
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " (y) * 3 + x",
"precedence": 1
}
},
"target": null,
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"seed": 83901550,
"simplified_expr": "( ((( 8 + 2))) * 3 + 9)",
"solutions_count": null,
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"⊗": null,
"⊙": null,
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"△": null,
"▽": {
"associativity": "left",
"conditions": [
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"condition": "y是3的倍数",
"operation": " x + y * x"
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],
"default_operation": " x + y",
"precedence": 4
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是奇数",
"operation": " x - x * y"
}
],
"default_operation": " 4 - x + x * y",
"precedence": 1
},
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " (y) * 3 + x",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "ed708792-69d3-4933-9045-d69824033c76"
},
"seed": 83901550,
"task_id": 283901550,
"task_type": "operation"
} |
logic-v2 | Define △, the rules are as follows:
when x and y are both even, x △ y = 5 + x - y ** y * x;
otherwise, x △ y = y + y - x - y - y.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 △ 4 △ 6 % 4
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 - abs(x + x).
and ☆, the rules are as follows:
when x and y are both odd, x ☆ y = y + y + x;
otherwise, x ☆ y = abs(y - x * y).
and ⊕, the rules are as follows:
when y is odd, x ⊕ y = y * x * y;
otherwise, x ⊕ y = abs(x / y).
The precedence of operations: ** = ⊕ > * = / = % = ☆ > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ⊕ 10 ⊗ 8 ☆ 9 * 6
Please fill your final answer in \boxed{}. | {
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"operation": " y + y + x"
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"precedence": 2
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"♢": null
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"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = y - abs(x + x).\nand ☆, the rules are as follows:\nwhen x and y are both odd, x ☆ y = y + y + x;\notherwise, x ☆ y = abs(y - x * y).\nand ⊕, the rules are as follows:\nwhen y is odd, x ⊕ y = y * x * y;\notherwise, x ⊕ y = abs(x / y).\nThe precedence of operations: ** = ⊕ > * = / = % = ☆ > + = - = ⊗。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 ⊕ 10 ⊗ 8 ☆ 9 * 6\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 = abs(y + x * y).
and ♡, the rules are as follows:
when x is even, x ♡ y = x □ y - x;
otherwise, x ♡ y = x - (y) - x.
The precedence of operations: □ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 □ 2
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 + x - y / x * x.
and □, the rules are as follows:
when x is equal to y, x □ y = x * (y + 3) ♢ 2;
otherwise, x □ y = x * 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 / y / x - x - y.
The precedence of operations: ** > * = / = % = ♢ = □ = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ♢ 4 □ 5 * 3 ○ 4 ○ 9
Please fill your final answer in \boxed{}. | {
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},
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"simplified_expr": "( 9 / 9 / (( 4 / 4 / ((((((( ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) + ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) - 5 / ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) * ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)))) / ((((10 + 10)) - ((((4 / 10)) * 10))))))) * 3)) - ((((((( ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) + ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) - 5 / ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) * ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)))) / ((((10 + 10)) - ((((4 / 10)) * 10))))))) * 3)) - 4)) - (( 4 / 4 / ((((((( ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) + ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) - 5 / ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) * ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)))) / ((((10 + 10)) - ((((4 / 10)) * 10))))))) * 3)) - ((((((( ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) + ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) - 5 / ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)) * ((((((10 + 10)) - ((((4 / 10)) * 10)))) * 5)))) / ((((10 + 10)) - ((((4 / 10)) * 10))))))) * 3)) - 4)) - 9)",
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logic-v2 | 定义 ◇，规则如下：
当y是偶数时，x ◇ y = x * y * 4；
其他情况下，x ◇ y = x * y。
和 ○，规则如下：
当x和y都是偶数时，x ○ y = x + (y) - x；
其他情况下，x ○ y = x / y - 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 ◇ x。
运算优先级：◇ = ○ = △ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 6 ◇ 3 ○ 4
请将最终答案填入\boxed{}中。 | {
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},
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"condition": "x和y都是偶数",
"operation": " x + (y) - x"
}
],
"default_operation": " x / y - x",
"precedence": 5
},
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logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * y * x.
and △, the rules are as follows:
when x and y are both even, x △ y = x * y + x;
otherwise, x △ y = x / y.
The precedence of operations: ⊙ = △ > ** = ⊗ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ⊙ 2 △ 4
Please fill your final answer in \boxed{}. | {
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},
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"default_operation": " y * y * x",
"precedence": 4
},
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"associativity": "left",
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"operation": " x * y + x"
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"precedence": 4
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"seed": 60548592,
"task_id": 260548592,
"task_type": "operation"
} |
logic-v2 | Define ○, the rules are as follows:
when y is a multiple of 5, x ○ y = x + x + y;
otherwise, x ○ y = y * abs(x).
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10
Please fill your final answer in \boxed{}. | {
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},
"metadata": {
"closing_sequence": null,
"expression": "10",
"fill_length": null,
"full_sequence": null,
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"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " x + x + y"
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logic-v2 | 定义 □，规则如下：
当x是奇数时，x □ y = y - x * x；
其他情况下，x □ y = x - x * y ** x。
和 ◎，规则如下：
实数域上，x ◎ y = x + 3 □ 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: 8 ◎ 5 □ 6 / 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 □，规则如下：\n当x是奇数时，x □ y = y - x * x；\n其他情况下，x □ y = x - x * y ** x。\n和 ◎，规则如下：\n实数域上，x ◎ y = x + 3 □ 2 * y。\n运算优先级：□ > ** > * = / = % = ◎ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 ◎ 5 □ 6 / 10\n请将最终答案填入\\boxed{}中。"
},
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"seed": 39681439,
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} |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y - x + x。
和 △，规则如下：
实数域上，x △ y = x + y。
运算优先级：□ > ** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 △ 9 % 3 - 7 □ 4
请将最终答案填入\boxed{}中。 | {
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"answer": "3",
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},
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logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = x + y + y + x.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ○ 5
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 = y + x / x。
和 ▽，规则如下：
当x和y都是奇数时，x ▽ y = x * (x * y)；
其他情况下，x ▽ y = (y * 5 + y * x / x)。
运算优先级：▽ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ** 3 ▽ 7 □ 7
请将最终答案填入\boxed{}中。 | {
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"question": "定义 □，规则如下：\n实数域上，x □ y = y + x / x。\n和 ▽，规则如下：\n当x和y都是奇数时，x ▽ y = x * (x * y)；\n其他情况下，x ▽ y = (y * 5 + y * x / x)。\n运算优先级：▽ > ** = □ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 ** 3 ▽ 7 □ 7\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"seed": 21371001,
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"condition": "x和y都是奇数",
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}
],
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},
"◇": null,
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"◎": null,
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"seed": 21371001,
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"task_type": "operation"
} |
logic-v2 | 定义 ◇，规则如下：
当y是3的倍数时，x ◇ y = x + x * x + y - x；
其他情况下，x ◇ y = y * x + 2 + 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: 6 ◇ 2
请将最终答案填入\boxed{}中。 | {
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"question_sequence": null,
"seed": 85621971,
"simplified_expr": "( 2 * 6 + 2 + 3)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "y是3的倍数",
"operation": " x + x * x + y - x"
}
],
"default_operation": " y * x + 2 + 3",
"precedence": 4
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "1537efc0-01d6-4cf8-af30-9510cf3915b2"
},
"question": "定义 ◇，规则如下：\n当y是3的倍数时，x ◇ y = x + x * x + y - x；\n其他情况下，x ◇ y = y * x + 2 + 3。\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 ◇ 2\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 85621971,
"simplified_expr": "( 2 * 6 + 2 + 3)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "y是3的倍数",
"operation": " x + x * x + y - x"
}
],
"default_operation": " y * x + 2 + 3",
"precedence": 4
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "1537efc0-01d6-4cf8-af30-9510cf3915b2"
},
"seed": 85621971,
"task_id": 285621971,
"task_type": "operation"
} |
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