env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = x / x / y.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 / 7 ○ 7 ○ 6
Please fill your final answer in \boxed{}. | {
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"expression": "3 / 7 ○ 7 ○ 6",
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"seed": 86867022,
"simplified_expr": "(3 / (( (( 7 / 7 / 7)) / (( 7 / 7 / 7)) / 6)))",
"solutions_count": null,
"symbol_definitions": {
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
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"conditions": [],
"default_operation": " x / x / y",
"precedence": 3
},
"◎": null,
"☆": null,
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},
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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: 3 / 7 ○ 7 ○ 6\nPlease fill your final answer in \\boxed{}."
},
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"expression": "3 / 7 ○ 7 ○ 6",
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"num_of_numbers": null,
"num_symbols": 1,
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"seed": 86867022,
"simplified_expr": "(3 / (( (( 7 / 7 / 7)) / (( 7 / 7 / 7)) / 6)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x / x / y",
"precedence": 3
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = x * x - y。
和 ⊗，规则如下：
当x是3的倍数时，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 = 1 + y * abs(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 ⊗ 7 ⊙ 1 ☆ 3
请将最终答案填入\boxed{}中。 | {
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"expression": "1 ⊗ 7 ⊙ 1 ☆ 3",
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"question_sequence": null,
"seed": 72865630,
"simplified_expr": "( 1 + 3 * abs((( (( (7 * 7 - 1))) * (( (7 * 7 - 1))) - 1))))",
"solutions_count": null,
"symbol_definitions": {
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"⊗": {
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"⊙": {
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"conditions": [],
"default_operation": " x * x - y",
"precedence": 4
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " 1 + y * abs(x)",
"precedence": 3
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "674d5d3f-3211-4775-8253-81439f01dac0"
},
"question": "定义 ⊙，规则如下：\n实数域上，x ⊙ y = x * x - y。\n和 ⊗，规则如下：\n当x是3的倍数时，x ⊗ y = x ** y ⊙ y；\n其他情况下，x ⊗ y = (y * y - x)。\n和 ☆，规则如下：\n实数域上，x ☆ y = 1 + y * abs(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 ⊗ 7 ⊙ 1 ☆ 3\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "1 ⊗ 7 ⊙ 1 ☆ 3",
"fill_length": null,
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"numbers": null,
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"seed": 72865630,
"simplified_expr": "( 1 + 3 * abs((( (( (7 * 7 - 1))) * (( (7 * 7 - 1))) - 1))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " x ** y ⊙ y"
}
],
"default_operation": " (y * y - x)",
"precedence": 4
},
"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " x * x - y",
"precedence": 4
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " 1 + y * abs(x)",
"precedence": 3
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "674d5d3f-3211-4775-8253-81439f01dac0"
},
"seed": 72865630,
"task_id": 272865630,
"task_type": "operation"
} |
logic-v2 | Define ⊗, the rules are as follows:
when the sum of x and y is even, x ⊗ y = 4 - x * y;
otherwise, x ⊗ y = x - y - abs(y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y - x * x - x.
and ◇, the rules are as follows:
when x and y are both even, x ◇ y = 3 * x ▽ x + y;
otherwise, x ◇ y = x ⊗ y + x - y.
The precedence of operations: ⊗ > ** > * = / = % = ◇ > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ▽ 6 ◇ 5 ⊗ 5
Please fill your final answer in \boxed{}. | {
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"expression": "1 ▽ 6 ◇ 5 ⊗ 5",
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 13263436,
"simplified_expr": "( ((((((( 6 - ((4 - ((5 * 5)))) - abs(((4 - ((5 * 5))))))) + 6)) - ((4 - ((5 * 5))))))) - 1 * 1 - 1)",
"solutions_count": null,
"symbol_definitions": {
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"conditions": [
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"operation": " 4 - x * y"
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],
"default_operation": " x - y - abs(y)",
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"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x * x - x",
"precedence": 1
},
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " 3 * x ▽ x + y"
}
],
"default_operation": " x ⊗ y + x - y",
"precedence": 2
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "166d551f-7b2d-4316-b077-2e128172e142"
},
"question": "Define ⊗, the rules are as follows:\nwhen the sum of x and y is even, x ⊗ y = 4 - x * y;\notherwise, x ⊗ y = x - y - abs(y).\nand ▽, the rules are as follows:\non the real number field, x ▽ y = y - x * x - x.\nand ◇, the rules are as follows:\nwhen x and y are both even, x ◇ y = 3 * x ▽ x + y;\notherwise, x ◇ y = x ⊗ y + x - y.\nThe precedence of operations: ⊗ > ** > * = / = % = ◇ > + = - = ▽。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 1 ▽ 6 ◇ 5 ⊗ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 6 ◇ 5 ⊗ 5",
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"seed": 13263436,
"simplified_expr": "( ((((((( 6 - ((4 - ((5 * 5)))) - abs(((4 - ((5 * 5))))))) + 6)) - ((4 - ((5 * 5))))))) - 1 * 1 - 1)",
"solutions_count": null,
"symbol_definitions": {
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"conditions": [
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"condition": "x和y的和是偶数",
"operation": " 4 - x * y"
}
],
"default_operation": " x - y - abs(y)",
"precedence": 4
},
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x * x - x",
"precedence": 1
},
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " 3 * x ▽ x + y"
}
],
"default_operation": " x ⊗ y + x - y",
"precedence": 2
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "166d551f-7b2d-4316-b077-2e128172e142"
},
"seed": 13263436,
"task_id": 213263436,
"task_type": "operation"
} |
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 △ 5
请将最终答案填入\boxed{}中。 | {
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"seed": 20856647,
"simplified_expr": "( 5 + 3 + 3 * 5 - 3)",
"solutions_count": null,
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"▽": null,
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"question": "定义 △，规则如下：\n实数域上，x △ y = y + x + x * y - x。\n运算优先级：** > * = / = % > + = - = △。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 △ 5\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "3 △ 5",
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"seed": 20856647,
"simplified_expr": "( 5 + 3 + 3 * 5 - 3)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x + x * y - x",
"precedence": 1
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
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"seed": 20856647,
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logic-v2 | 定义 ⊕，规则如下：
当x大于y时，x ⊕ y = y + y - x * x；
其他情况下，x ⊕ y = x - 5 * y。
和 ⊗，规则如下：
实数域上，x ⊗ y = 5 / y - x ⊕ x。
和 ◇，规则如下：
实数域上，x ◇ y = (y * x + y - y)。
运算优先级：⊕ > ** > * = / = % = ◇ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ⊗ 3 ⊕ 4 ◇ 9
请将最终答案填入\boxed{}中。 | {
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"gpt_response": "",
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"seed": 50706470,
"simplified_expr": "((((5 / ((((((9 * ((3 - ((5 * 4)))))) + 9)) - 9)))) - (( 10 - 5 * 10))))",
"solutions_count": null,
"symbol_definitions": {
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"conditions": [],
"default_operation": " 5 / y - x ⊕ x",
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"□": null,
"△": null,
"▽": null,
"◇": {
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"question": "定义 ⊕，规则如下：\n当x大于y时，x ⊕ y = y + y - x * x；\n其他情况下，x ⊕ y = x - 5 * y。\n和 ⊗，规则如下：\n实数域上，x ⊗ y = 5 / y - x ⊕ x。\n和 ◇，规则如下：\n实数域上，x ◇ y = (y * x + y - y)。\n运算优先级：⊕ > ** > * = / = % = ◇ > + = - = ⊗。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 ⊗ 3 ⊕ 4 ◇ 9\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "10 ⊗ 3 ⊕ 4 ◇ 9",
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"seed": 50706470,
"simplified_expr": "((((5 / ((((((9 * ((3 - ((5 * 4)))))) + 9)) - 9)))) - (( 10 - 5 * 10))))",
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"symbol_definitions": {
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],
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},
"⊗": {
"associativity": "left",
"conditions": [],
"default_operation": " 5 / y - x ⊕ x",
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},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " (y * x + y - y)",
"precedence": 2
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"trace_id": "4a765eac-8956-4f5c-a7ed-96682ac5b8de"
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"seed": 50706470,
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logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = 5 + 4 - y * x。
和 ⊕，规则如下：
实数域上，x ⊕ y = x ⊙ 1 * y。
和 ♡，规则如下：
当x和y都是偶数时，x ♡ y = x - abs(y) * y - y；
其他情况下，x ♡ y = x + y + 4 ⊙ y。
运算优先级：⊙ > ⊕ > ** > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊙ 3 * 3 ♡ 5 ⊕ 5
请将最终答案填入\boxed{}中。 | {
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"answer": "-402",
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"simplified_expr": "( (((( 5 + 4 - 3 * 1)) * 3)) - abs(((((( 5 + 4 - 1 * 5)) * 5)))) * ((((( 5 + 4 - 1 * 5)) * 5))) - ((((( 5 + 4 - 1 * 5)) * 5))))",
"solutions_count": null,
"symbol_definitions": {
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},
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [],
"default_operation": " 5 + 4 - y * x",
"precedence": 5
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " x - abs(y) * y - y"
}
],
"default_operation": " x + y + 4 ⊙ y",
"precedence": 2
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "b89593d4-1ffa-4361-a817-d1cf8299d970"
},
"question": "定义 ⊙，规则如下：\n实数域上，x ⊙ y = 5 + 4 - y * x。\n和 ⊕，规则如下：\n实数域上，x ⊕ y = x ⊙ 1 * y。\n和 ♡，规则如下：\n当x和y都是偶数时，x ♡ y = x - abs(y) * y - y；\n其他情况下，x ♡ y = x + y + 4 ⊙ 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 ⊙ 3 * 3 ♡ 5 ⊕ 5\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 3 * 3 ♡ 5 ⊕ 5",
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"simplified_expr": "( (((( 5 + 4 - 3 * 1)) * 3)) - abs(((((( 5 + 4 - 1 * 5)) * 5)))) * ((((( 5 + 4 - 1 * 5)) * 5))) - ((((( 5 + 4 - 1 * 5)) * 5))))",
"solutions_count": null,
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},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
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"condition": "x和y都是偶数",
"operation": " x - abs(y) * y - y"
}
],
"default_operation": " x + y + 4 ⊙ y",
"precedence": 2
},
"♢": null
},
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logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * 2 - y + x - y.
and ☆, the rules are as follows:
when y is a multiple of 3, x ☆ y = x + x * y;
otherwise, x ☆ y = 4 - y ⊕ 1 * 2 - x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y + 4 - x * 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: 2 ⊕ 4 ⊙ 8 ☆ 4
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "((((((((4 - ((((((((((1 * 2)) - 1)) + 4)) - 1)) * 2)))) - 8)) + 4)) - ((((((((((4 * 2)) - 4)) + 2)) - 4)) * (( 1 * 2 - 1 + ((((((((4 * 2)) - 4)) + 2)) - 4)) - 1))))))",
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
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"conditions": [
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"condition": "y是3的倍数",
"operation": " x + x * y"
}
],
"default_operation": " 4 - y ⊕ 1 * 2 - x",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "65552237-79ee-4f74-a483-ae2901432e8f"
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"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = y * 2 - y + x - y.\nand ☆, the rules are as follows:\nwhen y is a multiple of 3, x ☆ y = x + x * y;\notherwise, x ☆ y = 4 - y ⊕ 1 * 2 - x.\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = y + 4 - x * 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: 2 ⊕ 4 ⊙ 8 ☆ 4\nPlease fill your final answer in \\boxed{}."
},
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"expression": "2 ⊕ 4 ⊙ 8 ☆ 4",
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"seed": 27221009,
"simplified_expr": "((((((((4 - ((((((((((1 * 2)) - 1)) + 4)) - 1)) * 2)))) - 8)) + 4)) - ((((((((((4 * 2)) - 4)) + 2)) - 4)) * (( 1 * 2 - 1 + ((((((((4 * 2)) - 4)) + 2)) - 4)) - 1))))))",
"solutions_count": null,
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
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"operation": " x + x * y"
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],
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},
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"♢": null
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"seed": 27221009,
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} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = 3 ** y ** x.
and △, the rules are as follows:
when x is a multiple of 5, x △ y = y + y + 1 ☆ x;
otherwise, x △ y = 2 / x ☆ 5 / y.
The precedence of operations: ** = △ > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 1 ☆ 8 / 7
Please fill your final answer in \boxed{}. | {
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"○": null,
"◎": null,
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"conditions": [],
"default_operation": " 3 ** y ** x",
"precedence": 1
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"♡": null,
"♢": null
},
"target": null,
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"trace_id": "d978369c-e147-484a-8e9e-167bfc51b264"
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = 3 ** y ** x.\nand △, the rules are as follows:\nwhen x is a multiple of 5, x △ y = y + y + 1 ☆ x;\notherwise, x △ y = 2 / x ☆ 5 / y.\nThe precedence of operations: ** = △ > * = / = % > + = - = ☆。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 △ 1 ☆ 8 / 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "4 △ 1 ☆ 8 / 7",
"fill_length": null,
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"is_solvable": 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": 23709053,
"simplified_expr": "( 3 ** ((8 / 7)) ** ((( 3 ** ((5 / 1)) ** ((2 / 4))))))",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
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},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " 3 ** y ** x",
"precedence": 1
},
"♡": null,
"♢": null
},
"target": null,
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},
"seed": 23709053,
"task_id": 223709053,
"task_type": "operation"
} |
logic-v2 | Define ▽, 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: 7 ** 5 + 5 ▽ 6
Please fill your final answer in \boxed{}. | {
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"question": "Define ▽, the rules are as follows:\non the real number field, x ▽ y = y + x + x.\nThe precedence of operations: ** = ▽ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ** 5 + 5 ▽ 6\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "7 ** 5 + 5 ▽ 6",
"fill_length": null,
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"solutions_count": null,
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"default_operation": " y + x + x",
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},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"seed": 71696866,
"task_id": 271696866,
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} |
logic-v2 | 定义 ⊗，规则如下：
当x和y的和是奇数时，x ⊗ y = x / y / x * x；
其他情况下，x ⊗ y = y + x - x * y。
和 ⊕，规则如下：
实数域上，x ⊕ y = y * x ⊗ x * x。
和 ◇，规则如下：
实数域上，x ◇ y = 5 - y ⊕ x / y。
运算优先级：** = ⊕ > * = / = % = ⊗ = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ⊕ 7 ⊗ 9
请将最终答案填入\boxed{}中。 | {
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"▽": null,
"◇": {
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"conditions": [],
"default_operation": " 5 - y ⊕ x / y",
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"○": null,
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},
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"question": "定义 ⊗，规则如下：\n当x和y的和是奇数时，x ⊗ y = x / y / x * x；\n其他情况下，x ⊗ y = y + x - x * y。\n和 ⊕，规则如下：\n实数域上，x ⊕ y = y * x ⊗ x * x。\n和 ◇，规则如下：\n实数域上，x ◇ y = 5 - y ⊕ x / y。\n运算优先级：** = ⊕ > * = / = % = ⊗ = ◇ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 ⊕ 7 ⊗ 9\n请将最终答案填入\\boxed{}中。"
},
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"expression": "3 ⊕ 7 ⊗ 9",
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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 * x * x) + y。
和 ♢，规则如下：
实数域上，x ♢ y = abs(x) * y。
运算优先级：☆ = ♢ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♢ 4 ♢ 2 ☆ 3 - 8
请将最终答案填入\boxed{}中。 | {
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},
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"associativity": "left",
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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 = y * x + x。
和 △，规则如下：
当y是5的倍数时，x △ y = (x + y ♡ y)；
其他情况下，x △ y = y * y / x。
运算优先级：⊕ = ♡ > ** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♡ 10 ⊕ 6 △ 9
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊕，规则如下：\n当x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 = y * x + x。\n和 △，规则如下：\n当y是5的倍数时，x △ y = (x + y ♡ y)；\n其他情况下，x △ y = y * y / x。\n运算优先级：⊕ = ♡ > ** > * = / = % > + = - = △。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ♡ 10 ⊕ 6 △ 9\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 = 5 - 3 - x - (y)。
和 ○，规则如下：
当x是5的倍数时，x ○ y = y * y - x - y - (y)；
其他情况下，x ○ y = x / y + x * 3。
和 ☆，规则如下：
当y是5的倍数时，x ☆ y = y + x + x * y + x；
其他情况下，x ☆ y = y ○ 2 - 2 + x - y。
运算优先级：○ = ☆ > ** > * = / = % = ⊗ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ☆ 2 ⊗ 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = 5 - 3 - x - (y)。\n和 ○，规则如下：\n当x是5的倍数时，x ○ y = y * y - x - y - (y)；\n其他情况下，x ○ y = x / y + x * 3。\n和 ☆，规则如下：\n当y是5的倍数时，x ☆ y = y + x + x * y + x；\n其他情况下，x ☆ y = y ○ 2 - 2 + x - y。\n运算优先级：○ = ☆ > ** > * = / = % = ⊗ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 ☆ 2 ⊗ 4\n请将最终答案填入\\boxed{}中。"
},
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},
"seed": 56865575,
"task_id": 256865575,
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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 ○ 3 / 2 ○ 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 = x + x + y.\nThe precedence of operations: ** > * = / = % = ○ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ○ 3 / 2 ○ 4\nPlease fill your final answer in \\boxed{}."
},
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"seed": 4143541,
"simplified_expr": "( (((( 2 + 2 + 3)) / 2)) + (((( 2 + 2 + 3)) / 2)) + 4)",
"solutions_count": null,
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} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y * y - y + x / y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x ◎ y * x.
The precedence of operations: ◎ = ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ♡ 7
Please fill your final answer in \boxed{}. | {
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"seed": 95033389,
"simplified_expr": "(((( 7 * 7 - 7 + 2 / 7)) * 2))",
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"conditions": [],
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"♢": null
},
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = y * y - y + x / y.\nand ♡, the rules are as follows:\non the real number field, x ♡ y = x ◎ y * x.\nThe precedence of operations: ◎ = ♡ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ♡ 7\nPlease fill your final answer in \\boxed{}."
},
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"seed": 95033389,
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"◎": {
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"seed": 95033389,
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"task_type": "operation"
} |
logic-v2 | Define ○, the rules are as follows:
when the sum of x and y is even, x ○ y = x / y + y + y * y;
otherwise, x ○ y = x - y - y + y - x.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2
Please fill your final answer in \boxed{}. | {
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"gpt_response": "",
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"question": "Define ○, the rules are as follows:\nwhen the sum of x and y is even, x ○ y = x / y + y + y * y;\notherwise, x ○ y = x - y - y + y - x.\nThe precedence of operations: ○ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define ♢, the rules are as follows:
when x and y are both odd, x ♢ y = y + y - x;
otherwise, x ♢ y = y ** x - y.
and □, the rules are as follows:
when x is greater than y, x □ y = y + x - x;
otherwise, x □ y = y * x + x.
and ☆, the rules are as follows:
when x and y are both even, x ☆ y = (5 + 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: 1 ♢ 6 ☆ 9 □ 5 ♢ 7
Please fill your final answer in \boxed{}. | {
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"conditions": [
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"condition": "x和y都是偶数",
"operation": " (5 + x ** y)"
}
],
"default_operation": " y / x * x",
"precedence": 4
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " y + y - x"
}
],
"default_operation": " y ** x - y",
"precedence": 2
}
},
"target": null,
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"question": "Define ♢, the rules are as follows:\nwhen x and y are both odd, x ♢ y = y + y - x;\notherwise, x ♢ y = y ** x - y.\nand □, the rules are as follows:\nwhen x is greater than y, x □ y = y + x - x;\notherwise, x □ y = y * x + x.\nand ☆, the rules are as follows:\nwhen x and y are both even, x ☆ y = (5 + x ** y);\notherwise, x ☆ y = y / x * x.\nThe precedence of operations: ☆ > ** > * = / = % = ♢ > + = - = □。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 1 ♢ 6 ☆ 9 □ 5 ♢ 7\nPlease fill your final answer in \\boxed{}."
},
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"▽": null,
"◇": null,
"○": null,
"◎": null,
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"operation": " (5 + x ** y)"
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],
"default_operation": " y / x * x",
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},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
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"condition": "x和y都是奇数",
"operation": " y + y - x"
}
],
"default_operation": " y ** x - y",
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"seed": 56385244,
"task_id": 256385244,
"task_type": "operation"
} |
logic-v2 | 定义 ⊗，规则如下：
当y是5的倍数时，x ⊗ y = y - x * abs(y + 4)；
其他情况下，x ⊗ y = x + y / x * 2 * x。
和 ◎，规则如下：
实数域上，x ◎ y = x * y * x + x + x。
和 ♢，规则如下：
当x等于y时，x ♢ y = y ◎ y - x / x * y；
其他情况下，x ♢ y = x ⊗ x + y * x。
运算优先级：♢ > ** = ◎ > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊗ 3 ◎ 9 ♢ 5
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = x * y。
和 □，规则如下：
实数域上，x □ y = y ▽ x + (y)。
和 ♡，规则如下：
当x等于y时，x ♡ y = (y □ 5) * x；
其他情况下，x ♡ 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: 1 □ 6 ▽ 6 ♡ 8
请将最终答案填入\boxed{}中。 | {
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},
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"♢": null
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logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = abs(y * 2 / x).
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y + x + x + y。
和 ⊗，规则如下：
当y是3的倍数时，x ⊗ y = x - y ◎ 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 = 5 ◎ x - x ** y；
其他情况下，x ☆ y = 5 * (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: 2 % 3 ◎ 5 ☆ 8 ⊗ 1 * 8
请将最终答案填入\boxed{}中。 | {
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},
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],
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},
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"♢": null
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logic-v2 | Define ♢, the rules are as follows:
when x and y are both odd, x ♢ y = abs(y * 2 + x) + x;
otherwise, x ♢ y = x * y - 2 * x.
and ⊙, the rules are as follows:
when the sum of x and y is even, x ⊙ y = 2 * x + y;
otherwise, x ⊙ y = y + (y - x) + x.
and △, the rules are as follows:
on the real number field, x △ y = (y ⊙ x ** y).
The precedence of operations: ⊙ > ** = ♢ > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ⊙ 8 △ 2
Please fill your final answer in \boxed{}. | {
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"◎": null,
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"♡": null,
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"conditions": [
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"condition": "x和y都是奇数",
"operation": " abs(y * 2 + x) + x"
}
],
"default_operation": " x * y - 2 * x",
"precedence": 3
}
},
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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 = (y - x) + y.
and ♡, the rules are as follows:
when x and y are both odd, x ♡ y = (x - y) / y;
otherwise, x ♡ y = 5 - y * x.
and △, the rules are as follows:
when x is greater than y, 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: 1 ♢ 4 △ 7
Please fill your final answer in \boxed{}. | {
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"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
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"△": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " (x ♡ x + y)"
}
],
"default_operation": " (x * x ♢ y)",
"precedence": 4
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " (x - y) / y"
}
],
"default_operation": " 5 - y * x",
"precedence": 5
},
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " (y - x) + y",
"precedence": 4
}
},
"target": null,
"total_length": null,
"trace_id": "ad203453-3cde-40e6-b88f-5df5406f25fe"
},
"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = (y - x) + y.\nand ♡, the rules are as follows:\nwhen x and y are both odd, x ♡ y = (x - y) / y;\notherwise, x ♡ y = 5 - y * x.\nand △, the rules are as follows:\nwhen x is greater than y, x △ y = (x ♡ x + y);\notherwise, x △ y = (x * x ♢ y).\nThe precedence of operations: ♡ > ♢ = △ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 1 ♢ 4 △ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "1 ♢ 4 △ 7",
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"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 7763062,
"simplified_expr": "((((((4 - 1)) + 4)) * (( (7 - ((((4 - 1)) + 4))) + 7))))",
"solutions_count": null,
"symbol_definitions": {
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"△": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " (x ♡ x + y)"
}
],
"default_operation": " (x * x ♢ y)",
"precedence": 4
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " (x - y) / y"
}
],
"default_operation": " 5 - y * x",
"precedence": 5
},
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " (y - x) + y",
"precedence": 4
}
},
"target": null,
"total_length": null,
"trace_id": "ad203453-3cde-40e6-b88f-5df5406f25fe"
},
"seed": 7763062,
"task_id": 207763062,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x + y - y - x * y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 / 8 ▽ 2
Please fill your final answer in \boxed{}. | {
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"♢": null
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"question": "Define ▽, the rules are as follows:\non the real number field, x ▽ y = x + y - 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 / 8 ▽ 2\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "4 / 8 ▽ 2",
"fill_length": null,
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"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
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"operators": null,
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"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y - y - x * y",
"precedence": 4
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "fd91a033-799b-4f2e-8f62-89c12152f709"
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"seed": 20211282,
"task_id": 220211282,
"task_type": "operation"
} |
logic-v2 | 定义 ♡，规则如下：
当y是奇数时，x ♡ y = abs(4 * x * y)；
其他情况下，x ♡ y = x + x / y。
和 ▽，规则如下：
当y是5的倍数时，x ▽ y = y * x * y；
其他情况下，x ▽ y = 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: 5 ▽ 4 ▽ 7 ♡ 5 ♡ 8
请将最终答案填入\boxed{}中。 | {
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"operation": " y * x * y"
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],
"default_operation": " x + y ♡ 5",
"precedence": 5
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " abs(4 * x * y)"
}
],
"default_operation": " x + x / y",
"precedence": 2
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "138ac491-acb9-4ab2-acf9-36c0996ada2d"
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"question": "定义 ♡，规则如下：\n当y是奇数时，x ♡ y = abs(4 * x * y)；\n其他情况下，x ♡ y = x + x / y。\n和 ▽，规则如下：\n当y是5的倍数时，x ▽ y = y * x * y；\n其他情况下，x ▽ y = 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: 5 ▽ 4 ▽ 7 ♡ 5 ♡ 8\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 4 ▽ 7 ♡ 5 ♡ 8",
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"seed": 2810069,
"simplified_expr": "( (( (((((5 + (abs((((4 * 4)) * 5))))) + (( abs(4 * 7 * 5)))))) + (((((5 + (abs((((4 * 4)) * 5))))) + (( abs(4 * 7 * 5)))))) / 5)) + (( (((((5 + (abs((((4 * 4)) * 5))))) + (( abs(4 * 7 * 5)))))) + (((((5 + (abs((((4 * 4)) * 5))))) + (( abs(4 * 7 * 5)))))) / 5)) / 8)",
"solutions_count": null,
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"△": null,
"▽": {
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"conditions": [
{
"condition": "y是5的倍数",
"operation": " y * x * y"
}
],
"default_operation": " x + y ♡ 5",
"precedence": 5
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " abs(4 * x * y)"
}
],
"default_operation": " x + x / y",
"precedence": 2
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "138ac491-acb9-4ab2-acf9-36c0996ada2d"
},
"seed": 2810069,
"task_id": 202810069,
"task_type": "operation"
} |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x + x * y + 4。
和 ♢，规则如下：
实数域上，x ♢ y = y + x - y + x。
和 ⊙，规则如下：
当y是5的倍数时，x ⊙ y = x ○ (x) * 2 - y；
其他情况下，x ⊙ y = (x) + x * y + x。
运算优先级：♢ > ⊙ > ** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ⊙ 10 + 2 ○ 2 ♢ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "52",
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"default_operation": " (x) + x * y + x",
"precedence": 4
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x + x * y + 4",
"precedence": 2
},
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x - y + x",
"precedence": 5
}
},
"target": null,
"total_length": null,
"trace_id": "c9a47f1f-78e2-44b1-aade-7b8c97159c6f"
},
"question": "定义 ○，规则如下：\n实数域上，x ○ y = x + x * y + 4。\n和 ♢，规则如下：\n实数域上，x ♢ y = y + x - y + x。\n和 ⊙，规则如下：\n当y是5的倍数时，x ⊙ y = x ○ (x) * 2 - y；\n其他情况下，x ⊙ y = (x) + 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: 4 ⊙ 10 + 2 ○ 2 ♢ 1\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "4 ⊙ 10 + 2 ○ 2 ♢ 1",
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],
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},
"□": null,
"△": null,
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"◇": null,
"○": {
"associativity": "left",
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},
"◎": null,
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"♢": {
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"conditions": [],
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},
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},
"seed": 3416128,
"task_id": 203416128,
"task_type": "operation"
} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = abs(x * x) - y - y.
and △, the rules are as follows:
on the real number field, x △ y = y * y - 5 - x.
The precedence of operations: △ > ** > * = / = % = ☆ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ☆ 5 ☆ 5 △ 4
Please fill your final answer in \boxed{}. | {
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"expression": "9 ☆ 5 ☆ 5 △ 4",
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"n_types": null,
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"numbers": null,
"operators": null,
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"simplified_expr": "( abs((( abs(9 * 9) - 5 - 5)) * (( abs(9 * 9) - 5 - 5))) - (( 4 * 4 - 5 - 5)) - (( 4 * 4 - 5 - 5)))",
"solutions_count": null,
"symbol_definitions": {
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " abs(x * x) - y - y",
"precedence": 2
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "f7301127-f5b5-4bde-9826-537d5f4a235d"
},
"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = abs(x * x) - y - y.\nand △, the rules are as follows:\non the real number field, x △ y = y * y - 5 - x.\nThe precedence of operations: △ > ** > * = / = % = ☆ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 ☆ 5 ☆ 5 △ 4\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 5 ☆ 5 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 49181749,
"simplified_expr": "( abs((( abs(9 * 9) - 5 - 5)) * (( abs(9 * 9) - 5 - 5))) - (( 4 * 4 - 5 - 5)) - (( 4 * 4 - 5 - 5)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
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"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
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"♡": null,
"♢": null
},
"target": null,
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},
"seed": 49181749,
"task_id": 249181749,
"task_type": "operation"
} |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = x * 2 / y - y.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ○ 10 / 9
Please fill your final answer in \boxed{}. | {
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"△": null,
"▽": null,
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"○": {
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"☆": null,
"♡": null,
"♢": null
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"target": null,
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"question": "Define ○, the rules are as follows:\non the real number field, x ○ y = x * 2 / y - y.\nThe precedence of operations: ** > * = / = % = ○ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ○ 10 / 9\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 10 / 9",
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"is_solvable": null,
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"num_of_numbers": null,
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"operators": null,
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
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"default_operation": " x * 2 / y - y",
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},
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"seed": 24853862,
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} |
logic-v2 | Define ⊙, the rules are as follows:
when x and y are both even, x ⊙ y = y + x - 3;
otherwise, x ⊙ y = x / y - y.
and △, the rules are as follows:
on the real number field, x △ y = y + (y ⊙ x).
and ♡, the rules are as follows:
when y is a multiple of 5, x ♡ y = abs(y) - x + x;
otherwise, x ♡ y = (x * y ** 2).
The precedence of operations: ** = △ > * = / = % > + = - = ⊙ = ♡。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ♡ 6 ⊙ 4
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "253",
"difficulty": 1,
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"♡": {
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"condition": "y是5的倍数",
"operation": " abs(y) - x + x"
}
],
"default_operation": " (x * y ** 2)",
"precedence": 1
},
"♢": null
},
"target": null,
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"trace_id": "cca6424c-62d4-4f19-9f5e-967699f5334c"
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"question": "Define ⊙, the rules are as follows:\nwhen x and y are both even, x ⊙ y = y + x - 3;\notherwise, x ⊙ y = x / y - y.\nand △, the rules are as follows:\non the real number field, x △ y = y + (y ⊙ x).\nand ♡, the rules are as follows:\nwhen y is a multiple of 5, x ♡ y = abs(y) - x + x;\notherwise, x ♡ y = (x * y ** 2).\nThe precedence of operations: ** = △ > * = / = % > + = - = ⊙ = ♡。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ♡ 6 ⊙ 4\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x / y - x - y。
和 ♢，规则如下：
当y是奇数时，x ♢ y = (y ⊗ x * y + 5 * 3)；
其他情况下，x ♢ y = x + x / y。
和 ⊕，规则如下：
实数域上，x ⊕ y = abs(x + y) / 5 - x。
运算优先级：♢ > ** = ⊗ > * = / = % = ⊕ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ♢ 3 ⊕ 5 ⊗ 5
请将最终答案填入\boxed{}中。 | {
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"simplified_expr": "( abs(((((((( 3 / 8 - 3 - 8)) * 3)) + ((5 * 3))))) + (( 5 / 5 - 5 - 5))) / 5 - ((((((( 3 / 8 - 3 - 8)) * 3)) + ((5 * 3))))))",
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"♢": {
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"conditions": [
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"operation": " (y ⊗ x * y + 5 * 3)"
}
],
"default_operation": " x + x / y",
"precedence": 4
}
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = x / y - x - y。\n和 ♢，规则如下：\n当y是奇数时，x ♢ y = (y ⊗ x * y + 5 * 3)；\n其他情况下，x ♢ y = x + x / y。\n和 ⊕，规则如下：\n实数域上，x ⊕ y = abs(x + y) / 5 - x。\n运算优先级：♢ > ** = ⊗ > * = / = % = ⊕ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 ♢ 3 ⊕ 5 ⊗ 5\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "8 ♢ 3 ⊕ 5 ⊗ 5",
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"simplified_expr": "( abs(((((((( 3 / 8 - 3 - 8)) * 3)) + ((5 * 3))))) + (( 5 / 5 - 5 - 5))) / 5 - ((((((( 3 / 8 - 3 - 8)) * 3)) + ((5 * 3))))))",
"solutions_count": null,
"symbol_definitions": {
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"conditions": [],
"default_operation": " x / y - x - y",
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},
"⊙": null,
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"△": null,
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"operation": " (y ⊗ x * y + 5 * 3)"
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],
"default_operation": " x + x / y",
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"seed": 26942913,
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"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x / y + y.
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{}. | {
"game_data": {
"answer": "4.5",
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"expression": "5 ◇ 2",
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"♢": null
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"target": null,
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"trace_id": "86bc42d7-4ff3-4866-b73b-d6de35763983"
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"question": "Define ◇, the rules are as follows:\non the real number field, x ◇ y = x / y + y.\nThe precedence of operations: ** > * = / = % > + = - = ◇。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ◇ 2\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 2",
"fill_length": null,
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"num_of_numbers": null,
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"simplified_expr": "( 5 / 2 + 2)",
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"symbol_definitions": {
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"△": null,
"▽": null,
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"conditions": [],
"default_operation": " x / y + y",
"precedence": 1
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "86bc42d7-4ff3-4866-b73b-d6de35763983"
},
"seed": 76149750,
"task_id": 276149750,
"task_type": "operation"
} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x - y + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y * y * x.
The precedence of operations: ** > * = / = % = ☆ > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ⊗ 10 ☆ 9
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "726",
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"expression": "6 ⊗ 10 ☆ 9",
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"numbers": null,
"operators": null,
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"seed": 98432373,
"simplified_expr": "( (( 10 - 9 + 10)) * (( 10 - 9 + 10)) * 6)",
"solutions_count": null,
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y + x",
"precedence": 2
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "77984653-1987-4a6f-b797-4c93539655a6"
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = x - y + x.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = y * y * x.\nThe precedence of operations: ** > * = / = % = ☆ > + = - = ⊗。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 ⊗ 10 ☆ 9\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 10 ☆ 9",
"fill_length": null,
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"is_solvable": null,
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"num_of_numbers": null,
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"numbers": null,
"operators": null,
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"seed": 98432373,
"simplified_expr": "( (( 10 - 9 + 10)) * (( 10 - 9 + 10)) * 6)",
"solutions_count": null,
"symbol_definitions": {
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"⊗": {
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"conditions": [],
"default_operation": " y * y * x",
"precedence": 1
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y + x",
"precedence": 2
},
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"♢": null
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"target": null,
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"trace_id": "77984653-1987-4a6f-b797-4c93539655a6"
},
"seed": 98432373,
"task_id": 298432373,
"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y + x * x - y / x.
and △, the rules are as follows:
on the real number field, x △ y = x ◎ x * 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: 10 △ 4
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "420",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 4",
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"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 60904604,
"simplified_expr": "(((((( 10 + 10 * 10 - 10 / 10)) * 4)) - ((4 * 4))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
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"△": {
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"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x * x - y / x",
"precedence": 5
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "90a8d010-149f-4b53-a203-dfb828d8d8b6"
},
"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = y + x * x - y / x.\nand △, the rules are as follows:\non the real number field, x △ y = x ◎ x * 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: 10 △ 4\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "10 △ 4",
"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": 60904604,
"simplified_expr": "(((((( 10 + 10 * 10 - 10 / 10)) * 4)) - ((4 * 4))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
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"default_operation": " x ◎ x * y - y * y",
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},
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"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x * x - y / x",
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"☆": null,
"♡": null,
"♢": null
},
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"trace_id": "90a8d010-149f-4b53-a203-dfb828d8d8b6"
},
"seed": 60904604,
"task_id": 260904604,
"task_type": "operation"
} |
logic-v2 | Define ⊙, the rules are as follows:
when x is even, x ⊙ y = x ** x * y;
otherwise, x ⊙ y = y + x * x.
and ♡, 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.
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 ⊙ 6 ☆ 10
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "1397",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 8 ⊙ 6 ☆ 10",
"fill_length": null,
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"n_types": null,
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"num_of_numbers": null,
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"numbers": null,
"operators": null,
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"simplified_expr": "( (( 6 + (( 5 - 8 - 8)) * (( 5 - 8 - 8)))) + 10 * (( 6 + (( 5 - 8 - 8)) * (( 5 - 8 - 8)))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
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"default_operation": " y + x * x",
"precedence": 2
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y * x",
"precedence": 1
},
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y - y",
"precedence": 4
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "f25e746d-b6e2-4f39-bfac-d3a094000a75"
},
"question": "Define ⊙, the rules are as follows:\nwhen x is even, x ⊙ y = x ** x * y;\notherwise, x ⊙ y = y + x * x.\nand ♡, 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.\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 ⊙ 6 ☆ 10\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 8 ⊙ 6 ☆ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 35724179,
"simplified_expr": "( (( 6 + (( 5 - 8 - 8)) * (( 5 - 8 - 8)))) + 10 * (( 6 + (( 5 - 8 - 8)) * (( 5 - 8 - 8)))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " x ** x * y"
}
],
"default_operation": " y + x * x",
"precedence": 2
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y * x",
"precedence": 1
},
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y - y",
"precedence": 4
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "f25e746d-b6e2-4f39-bfac-d3a094000a75"
},
"seed": 35724179,
"task_id": 235724179,
"task_type": "operation"
} |
logic-v2 | 定义 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = (y * y + x - x) - y；
其他情况下，x ⊗ y = x - (x * y * y) / x。
和 ◎，规则如下：
实数域上，x ◎ y = y - y * x * y。
和 ♢，规则如下：
当x和y的和是偶数时，x ♢ y = 1 / x ⊗ y - y * y；
其他情况下，x ♢ y = 4 * 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 ♢ 1 ◎ 6 % 10 ⊗ 9
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 △，规则如下：
当y是5的倍数时，x △ y = 5 - y + 1 - x - y；
其他情况下，x △ y = (x * y * x / x + y)。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 * 3 △ 2 ** 6
请将最终答案填入\boxed{}中。 | {
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"question": "定义 △，规则如下：\n当y是5的倍数时，x △ y = 5 - y + 1 - x - y；\n其他情况下，x △ y = (x * y * x / x + y)。\n运算优先级：** > * = / = % = △ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2 * 3 △ 2 ** 6\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = 5 - 1 - x * 4 * y。
和 ▽，规则如下：
当y是偶数时，x ▽ y = y + x；
其他情况下，x ▽ y = y - 4 * 2 * 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: 10 ♡ 5 ▽ 4 ▽ 7 % 3
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ♡，规则如下：\n实数域上，x ♡ y = 5 - 1 - x * 4 * y。\n和 ▽，规则如下：\n当y是偶数时，x ▽ y = y + x；\n其他情况下，x ▽ y = y - 4 * 2 * 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: 10 ♡ 5 ▽ 4 ▽ 7 % 3\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | Define ◎, the rules are as follows:
when the sum of x and y is even, x ◎ y = y * y - x;
otherwise, x ◎ y = y + (y * x).
The precedence of operations: ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ◎ 6
Please fill your final answer in \boxed{}. | {
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"question": "Define ◎, the rules are as follows:\nwhen the sum of x and y is even, x ◎ y = y * y - x;\notherwise, x ◎ y = y + (y * x).\nThe precedence of operations: ** = ◎ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 ◎ 6\nPlease fill your final answer in \\boxed{}."
},
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"○": null,
"◎": {
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logic-v2 | Define ⊕, the rules are as follows:
when x is less than y, x ⊕ y = x * x - y + x;
otherwise, x ⊕ y = 3 / abs(y + x) + y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x - y + x + y.
and ◇, the rules are as follows:
when x is equal to y, x ◇ y = y + x - y ⊕ y;
otherwise, x ◇ y = y * y + x.
The precedence of operations: ⊕ > ** = ⊗ > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ⊗ 2 ⊕ 3
Please fill your final answer in \boxed{}. | {
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"operation": " y + x - y ⊕ y"
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],
"default_operation": " y * y + x",
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"○": null,
"◎": null,
"☆": null,
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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 * x - y + x;\notherwise, x ⊕ y = 3 / abs(y + x) + y.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = x - y + x + y.\nand ◇, the rules are as follows:\nwhen x is equal to y, x ◇ y = y + x - y ⊕ y;\notherwise, x ◇ y = y * y + x.\nThe precedence of operations: ⊕ > ** = ⊗ > * = / = % > + = - = ◇。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ⊗ 2 ⊕ 3\nPlease fill your final answer in \\boxed{}."
},
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"precedence": 3
},
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"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
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"condition": "x等于y",
"operation": " y + x - y ⊕ y"
}
],
"default_operation": " y * y + x",
"precedence": 1
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "12fc091d-98fc-4b90-bed3-61ebfffe1844"
},
"seed": 82777839,
"task_id": 282777839,
"task_type": "operation"
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logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y - abs(x) * y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (x) □ x * y.
and ♢, the rules are as follows:
on the real number field, x ♢ y = 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 ♢ 1 ☆ 6 □ 2
Please fill your final answer in \boxed{}. | {
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"♡": null,
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"associativity": "left",
"conditions": [],
"default_operation": " x * x * y",
"precedence": 1
}
},
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"question": "Define □, the rules are as follows:\non the real number field, x □ y = y - abs(x) * y.\nand ☆, 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 * 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 ♢ 1 ☆ 6 □ 2\nPlease fill your final answer in \\boxed{}."
},
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"seed": 8070096,
"simplified_expr": "( 2 - abs(((( ((((((4 * 4)) * 1)) * 6)) - abs(((((4 * 4)) * 1))) * ((((((4 * 4)) * 1)) * 6)))))) * 2)",
"solutions_count": null,
"symbol_definitions": {
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"□": {
"associativity": "left",
"conditions": [],
"default_operation": " y - abs(x) * y",
"precedence": 1
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " (x) □ x * y",
"precedence": 1
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " x * x * y",
"precedence": 1
}
},
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"trace_id": "d01b31ff-47cf-49a2-9d2f-022cd66304fd"
},
"seed": 8070096,
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logic-v2 | 定义 ▽，规则如下：
当y是3的倍数时，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 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
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"expression": "5 ▽ 8",
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"conditions": [
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"default_operation": " x - y + y",
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"trace_id": "188b8e20-da1a-4bcd-bc43-e09721135cba"
},
"question": "定义 ▽，规则如下：\n当y是3的倍数时，x ▽ y = x * x - y；\n其他情况下，x ▽ y = x - y + y。\n运算优先级：** > * = / = % > + = - = ▽。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 ▽ 8\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 8",
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"△": null,
"▽": {
"associativity": "left",
"conditions": [
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"operation": " x * x - y"
}
],
"default_operation": " x - y + y",
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"seed": 89636723,
"task_id": 289636723,
"task_type": "operation"
} |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x ** x / y / x。
和 ⊙，规则如下：
当x是5的倍数时，x ⊙ y = y + (y - x □ x) / y；
其他情况下，x ⊙ y = y * x + x + x - (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: 9 □ 6 * 8 % 3 ⊙ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 6 * 8 % 3 ⊙ 5",
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"numbers": null,
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"operation": " y + (y - x □ x) / y"
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"default_operation": " y * x + x + x - (3)",
"precedence": 5
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"□": {
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"default_operation": " x ** x / y / x",
"precedence": 4
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"△": null,
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"◇": null,
"○": null,
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"☆": null,
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"♢": null
},
"target": null,
"total_length": null,
"trace_id": "a454d351-5863-4ece-8843-590507cea5bc"
},
"question": "定义 □，规则如下：\n实数域上，x □ y = x ** x / y / x。\n和 ⊙，规则如下：\n当x是5的倍数时，x ⊙ y = y + (y - x □ x) / y；\n其他情况下，x ⊙ y = y * x + x + x - (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: 9 □ 6 * 8 % 3 ⊙ 5\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "9 □ 6 * 8 % 3 ⊙ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 73467506,
"simplified_expr": "((((( 9 ** 9 / 6 / 9)) * 8)) % (( 5 * 3 + 3 + 3 - (3))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": {
"associativity": "left",
"conditions": [
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"condition": "x是5的倍数",
"operation": " y + (y - x □ x) / y"
}
],
"default_operation": " y * x + x + x - (3)",
"precedence": 5
},
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " x ** x / y / x",
"precedence": 4
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "a454d351-5863-4ece-8843-590507cea5bc"
},
"seed": 73467506,
"task_id": 273467506,
"task_type": "operation"
} |
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