env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * x + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y + y + x.
and △, the rules are as follows:
on the real number field, x △ y = x - x - x ⊙ y.
The precedence of operations: △ > ** = ◎ > * = / = % > + = - = ⊙。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ⊙ 7 △ 9 ◎ 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 = y * x + y.\nand ◎, the rules are as follows:\non the real number field, x ◎ y = y + y + x.\nand △, the rules are as follows:\non the real number field, x △ y = x - x - x ⊙ y.\nThe precedence of operations: △ > ** = ◎ > * = / = % > + = - = ⊙。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ⊙ 7 △ 9 ◎ 7\nPlease fill your final answer in \\boxed{}."
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"simplified_expr": "( (( 7 + 7 + ((( 9 * ((((7 - 7)) - 7)) + 9))))) * 3 + (( 7 + 7 + ((( 9 * ((((7 - 7)) - 7)) + 9))))))",
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logic-v2 | 定义 △，规则如下：
实数域上，x △ y = abs(y - y + x) / y。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 - 6 % 7 △ 2
请将最终答案填入\boxed{}中。 | {
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"question": "定义 △，规则如下：\n实数域上，x △ y = abs(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: 9 - 6 % 7 △ 2\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等于y时，x ♢ y = x * y + x * 5；
其他情况下，x ♢ y = y * 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 * 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 / 4 ⊕ 1 ♢ 5 ⊗ 3
请将最终答案填入\boxed{}中。 | {
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"simplified_expr": "( ((9 / 4)) * (( (((5 - (( 3 * 5 + 3))))) * 1 + (((5 - (( 3 * 5 + 3))))))) - ((9 / 4)) - ((9 / 4)))",
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"question": "定义 ♢，规则如下：\n当x等于y时，x ♢ y = x * y + x * 5；\n其他情况下，x ♢ y = y * 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 * y - x - x。\n运算优先级：⊗ > ** > * = / = % = ♢ > + = - = ⊕。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 9 / 4 ⊕ 1 ♢ 5 ⊗ 3\n请将最终答案填入\\boxed{}中。"
},
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"simplified_expr": "( ((9 / 4)) * (( (((5 - (( 3 * 5 + 3))))) * 1 + (((5 - (( 3 * 5 + 3))))))) - ((9 / 4)) - ((9 / 4)))",
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logic-v2 | 定义 □，规则如下：
当x和y都是奇数时，x □ y = x - y + y；
其他情况下，x □ y = y + y + y * x。
和 ○，规则如下：
当x是奇数时，x ○ y = (x - x) + y；
其他情况下，x ○ y = y - y □ x。
运算优先级：□ > ** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ○ 8
请将最终答案填入\boxed{}中。 | {
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"question": "定义 □，规则如下：\n当x和y都是奇数时，x □ y = x - y + y；\n其他情况下，x □ y = y + y + y * x。\n和 ○，规则如下：\n当x是奇数时，x ○ y = (x - x) + y；\n其他情况下，x ○ y = y - y □ x。\n运算优先级：□ > ** > * = / = % = ○ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 ○ 8\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 odd, x ○ y = y ** x * 5 * y;
otherwise, x ○ y = (y) + x * y - y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x - x - y - x.
The precedence of operations: ** > * = / = % = ○ = ☆ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ☆ 9 ○ 7 / 4
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "((( 7 ** (( 9 - 9 - 9 - 9)) * 5 * 7)) / 4)",
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"simplified_expr": "((( 7 ** (( 9 - 9 - 9 - 9)) * 5 * 7)) / 4)",
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logic-v2 | Define ○, the rules are as follows:
when x is greater than y, x ○ y = y + x + y + x + y;
otherwise, x ○ y = y - y + x - x * x.
and ⊙, the rules are as follows:
when x is even, x ⊙ y = x / 5 + y + y / y;
otherwise, x ⊙ y = y - 3 + y * x - x.
and ▽, the rules are as follows:
when y is a multiple of 5, x ▽ y = x ⊙ y + (5 + y ** y);
otherwise, x ▽ y = y ⊙ y * y + y - x.
The precedence of operations: ○ > ▽ > ** > * = / = % > + = - = ⊙。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ⊙ 10 ○ 10
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "( 2 / 5 + (( 10 - 10 + 10 - 10 * 10)) + (( 10 - 10 + 10 - 10 * 10)) / (( 10 - 10 + 10 - 10 * 10)))",
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"△": null,
"▽": {
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"conditions": [
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"condition": "y是5的倍数",
"operation": " x ⊙ y + (5 + y ** y)"
}
],
"default_operation": " y ⊙ y * y + y - x",
"precedence": 4
},
"◇": null,
"○": {
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"conditions": [
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"condition": "x大于y",
"operation": " y + x + y + x + y"
}
],
"default_operation": " y - y + x - x * x",
"precedence": 5
},
"◎": null,
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"question": "Define ○, the rules are as follows:\nwhen x is greater than y, x ○ y = y + x + y + x + y;\notherwise, x ○ y = y - y + x - x * x.\nand ⊙, the rules are as follows:\nwhen x is even, x ⊙ y = x / 5 + y + y / y;\notherwise, x ⊙ y = y - 3 + y * x - x.\nand ▽, the rules are as follows:\nwhen y is a multiple of 5, x ▽ y = x ⊙ y + (5 + y ** y);\notherwise, x ▽ y = y ⊙ y * y + y - x.\nThe precedence of operations: ○ > ▽ > ** > * = / = % > + = - = ⊙。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ⊙ 10 ○ 10\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 = abs(y * 4) + x;
otherwise, x ○ y = y * y + x / y.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ○ 7
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(y * 4) + x;\notherwise, x ○ y = y * y + x / y.\nThe precedence of operations: ○ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ○ 7\nPlease fill your final answer in \\boxed{}."
},
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"○": {
"associativity": "left",
"conditions": [
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"condition": "y是3的倍数",
"operation": " abs(y * 4) + x"
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"default_operation": " y * y + x / y",
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"seed": 19659699,
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} |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x - (x - y + x) * x。
和 ▽，规则如下：
当y是奇数时，x ▽ y = y ☆ y / x；
其他情况下，x ▽ y = y / x / x ☆ x + y。
运算优先级：☆ > ** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ☆ 5 ▽ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4.000476",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"expression": "5 ☆ 5 ▽ 4",
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],
"default_operation": " y / x / x ☆ x + y",
"precedence": 3
},
"◇": null,
"○": null,
"◎": null,
"☆": {
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"conditions": [],
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"question": "定义 ☆，规则如下：\n实数域上，x ☆ y = x - (x - y + x) * x。\n和 ▽，规则如下：\n当y是奇数时，x ▽ y = y ☆ y / x；\n其他情况下，x ▽ y = y / x / x ☆ x + y。\n运算优先级：☆ > ** = ▽ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 ☆ 5 ▽ 4\n请将最终答案填入\\boxed{}中。"
},
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"operation": " y ☆ y / x"
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],
"default_operation": " y / x / x ☆ x + y",
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},
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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 - abs(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: 5 ○ 3
请将最终答案填入\boxed{}中。 | {
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},
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"seed": 7679239,
"simplified_expr": "( 3 - 5 - 5)",
"solutions_count": null,
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"seed": 7679239,
"task_id": 207679239,
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} |
logic-v2 | Define △, the rules are as follows:
when x is greater than y, x △ y = 1 / (y) + x;
otherwise, x △ y = y + x - x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 △ 4
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "6.25",
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"gpt_response": "",
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},
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logic-v2 | 定义 ◇，规则如下：
当x大于y时，x ◇ y = y + y / x；
其他情况下，x ◇ y = x - 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: 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"fill_length": null,
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"question": "定义 ◇，规则如下：\n当x大于y时，x ◇ y = y + y / x；\n其他情况下，x ◇ y = x - x - y + 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\n请将最终答案填入\\boxed{}中。"
},
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"◇": {
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logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x * abs(x) - y - y / x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x - y + 2 □ y.
The precedence of operations: ** = ⊗ > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ⊗ 1 □ 1 ⊗ 6
Please fill your final answer in \boxed{}. | {
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"associativity": "left",
"conditions": [],
"default_operation": " x * abs(x) - y - y / x",
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},
"△": null,
"▽": null,
"◇": null,
"○": null,
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},
"target": null,
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"trace_id": "55212e5d-19e4-441a-8a8d-1d21dafbb307"
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"question": "Define □, the rules are as follows:\non the real number field, x □ y = x * abs(x) - y - y / x.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = x - y + 2 □ y.\nThe precedence of operations: ** = ⊗ > * = / = % = □ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 ⊗ 1 □ 1 ⊗ 6\nPlease fill your final answer in \\boxed{}."
},
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"expression": "10 ⊗ 1 □ 1 ⊗ 6",
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"simplified_expr": "( (((((10 - 1)) + (( 2 * abs(2) - 1 - 1 / 2))))) * abs((((((10 - 1)) + (( 2 * abs(2) - 1 - 1 / 2)))))) - (((((1 - 6)) + (( 2 * abs(2) - 6 - 6 / 2))))) - (((((1 - 6)) + (( 2 * abs(2) - 6 - 6 / 2))))) / (((((10 - 1)) + (( 2 * abs(2) - 1 - 1 / 2))))))",
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logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - y + y / y - x.
and □, the rules are as follows:
on the real number field, x □ y = 5 / x ⊙ y * x * 4.
and ☆, the rules are as follows:
when the sum of x and y is even, x ☆ y = y - y - x;
otherwise, x ☆ y = y + abs(y) / x.
The precedence of operations: ☆ > ⊙ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ⊙ 1 ☆ 10
Please fill your final answer in \boxed{}. | {
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"operation": " y - y - x"
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"precedence": 5
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"question": "Define ⊙, the rules are as follows:\non the real number field, x ⊙ y = y - y + y / y - x.\nand □, the rules are as follows:\non the real number field, x □ y = 5 / x ⊙ y * x * 4.\nand ☆, the rules are as follows:\nwhen the sum of x and y is even, x ☆ y = y - y - x;\notherwise, x ☆ y = 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: 8 ⊙ 1 ☆ 10\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( (( 10 + abs(10) / 1)) - (( 10 + abs(10) / 1)) + (( 10 + abs(10) / 1)) / (( 10 + abs(10) / 1)) - 8)",
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"conditions": [],
"default_operation": " 5 / x ⊙ y * x * 4",
"precedence": 2
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"▽": null,
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"operation": " y - y - x"
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"♢": null
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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) + 4；
其他情况下，x ◇ y = (y * x)。
运算优先级：** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◇，规则如下：\n当x和y的和是偶数时，x ◇ y = (x * y) + 4；\n其他情况下，x ◇ y = (y * x)。\n运算优先级：** > * = / = % = ◇ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 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y是偶数时，x ◎ y = y + x - x + y * 2；
其他情况下，x ◎ y = y * y * x ** x * x。
和 ♡，规则如下：
当x和y的和是奇数时，x ♡ y = x + x * y + x ◎ x；
其他情况下，x ♡ y = 4 / y ◎ (x + x + 5)。
运算优先级：** = ◎ > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◎ 1
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◎，规则如下：\n当y是偶数时，x ◎ y = y + x - x + y * 2；\n其他情况下，x ◎ y = y * y * x ** x * x。\n和 ♡，规则如下：\n当x和y的和是奇数时，x ♡ y = x + x * y + x ◎ x；\n其他情况下，x ♡ y = 4 / y ◎ (x + x + 5)。\n运算优先级：** = ◎ > * = / = % = ♡ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 ◎ 1\n请将最终答案填入\\boxed{}中。"
},
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"operation": " x + x * y + x ◎ x"
}
],
"default_operation": " 4 / y ◎ (x + x + 5)",
"precedence": 2
},
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},
"seed": 82221735,
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"task_type": "operation"
} |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = abs(y) + x - x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 % 9 △ 1 * 5
Please fill your final answer in \boxed{}. | {
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},
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"○": null,
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"seed": 48450994,
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logic-v2 | Define ☆, the rules are as follows:
when x is equal to y, x ☆ y = y ** 4 / (3 + 1) ** x;
otherwise, x ☆ y = y * y * x - y * x.
and ⊕, the rules are as follows:
when x is even, x ⊕ y = 3 * x / y + 1 ☆ 5;
otherwise, x ⊕ 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: 5 ⊕ 7 ☆ 9
Please 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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"operation": " y ** 4 / (3 + 1) ** x"
}
],
"default_operation": " y * y * x - y * x",
"precedence": 2
},
"♡": null,
"♢": null
},
"target": null,
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},
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"☆": {
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}
],
"default_operation": " y * y * x - y * x",
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},
"♡": null,
"♢": null
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"target": null,
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},
"seed": 2483067,
"task_id": 202483067,
"task_type": "operation"
} |
logic-v2 | 定义 △，规则如下：
当x小于y时，x △ y = y - x + y；
其他情况下，x △ y = y ** y + x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 2 % 4 + 8
请将最终答案填入\boxed{}中。 | {
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"question": "定义 △，规则如下：\n当x小于y时，x △ y = y - x + y；\n其他情况下，x △ y = y ** y + x。\n运算优先级：△ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 △ 2 % 4 + 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 - x - (y + x) * y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y - x + y * y ♢ y.
and △, the rules are as follows:
on the real number field, x △ y = abs(2 / x - x) / x - y.
The precedence of operations: △ > ** > * = / = % > + = - = ♢ = ⊕。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ♢ 9 ⊕ 6 % 3 ⊕ 2 △ 7
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = (x * y)。
和 ☆，规则如下：
当y是偶数时，x ☆ y = abs(x - x) - y；
其他情况下，x ☆ y = y - y / x。
和 ○，规则如下：
当x大于y时，x ○ y = x * (y)；
其他情况下，x ○ y = x * y。
运算优先级：♢ = ☆ = ○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ○ 7 ☆ 5 ♢ 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是奇数时，x ◇ y = abs(y / x)；
其他情况下，x ◇ y = 3 * x + y。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y ** y - x - x.
and ◇, the rules are as follows:
when x is odd, x ◇ y = y / x / y ♢ x;
otherwise, x ◇ y = (x) / y - 2.
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: 3 ◇ 8 ♢ 6
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 * 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: 4 ♡ 6 ♢ 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ♡，规则如下：\n实数域上，x ♡ y = y + x * y。\n和 ♢，规则如下：\n实数域上，x ♢ y = y * x - x。\n运算优先级：♡ > ** > * = / = % > + = - = ♢。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ♡ 6 ♢ 10\n请将最终答案填入\\boxed{}中。"
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logic-v2 | Define ⊕, the rules are as follows:
when y is a multiple of 5, x ⊕ y = y + y - y * 5 + x;
otherwise, x ⊕ y = abs(y * 4) - x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * y - x + x * x.
The precedence of operations: ⊙ > ** > * = / = % > + = - = ⊕。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ⊙ 5
Please fill your final answer in \boxed{}. | {
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},
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"seed": 32067948,
"simplified_expr": "( 5 * 5 - 6 + 6 * 6)",
"solutions_count": null,
"symbol_definitions": {
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"seed": 32067948,
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} |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x / abs(y) + y.
and ◇, the rules are as follows:
when x is a multiple of 5, x ◇ y = y / y - y + x + x;
otherwise, x ◇ y = 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 ▽ 3 ◇ 7
Please fill your final answer in \boxed{}. | {
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"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"question": "Define ▽, the rules are as follows:\non the real number field, x ▽ y = x / abs(y) + y.\nand ◇, the rules are as follows:\nwhen x is a multiple of 5, x ◇ y = y / y - y + x + x;\notherwise, x ◇ y = 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 ▽ 3 ◇ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "6 ▽ 3 ◇ 7",
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"seed": 67459197,
"simplified_expr": "( 7 / 7 + 7 * (( 6 / abs(3) + 3)) + (( 6 / abs(3) + 3)))",
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"symbol_definitions": {
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"condition": "x是5的倍数",
"operation": " y / y - y + x + x"
}
],
"default_operation": " y / y + y * x + x",
"precedence": 1
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "3bf47460-a448-4c54-9db4-b79de1a80ee7"
},
"seed": 67459197,
"task_id": 267459197,
"task_type": "operation"
} |
logic-v2 | 定义 ⊕，规则如下：
当x和y的和是奇数时，x ⊕ y = y - x + x；
其他情况下，x ⊕ y = y + y + 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 + 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 ⊕ 4 ○ 4 ⊙ 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 = y - x + x；\n其他情况下，x ⊕ y = y + y + x。\n和 ⊙，规则如下：\n实数域上，x ⊙ y = y ** (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: 8 ⊕ 3 ⊕ 4 ○ 4 ⊙ 1\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"seed": 40023301,
"simplified_expr": "( (( 1 ** (1 * 4))) + (( 4 - (( 3 - 8 + 8)) + (( 3 - 8 + 8)))) - (( 1 ** (1 * 4))))",
"solutions_count": null,
"symbol_definitions": {
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},
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"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x - y",
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},
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"♡": null,
"♢": null
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"seed": 40023301,
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logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x - y * x * 2 - y.
and △, the rules are as follows:
on the real number field, x △ y = 2 + 2 + y * x - x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y + x + 2.
The precedence of operations: △ = ◇ > ** > * = / = % > + = - = □。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ◇ 1 △ 9 □ 2
Please fill your final answer in \boxed{}. | {
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"seed": 58545156,
"simplified_expr": "( (( 2 + 2 + 9 * (( 1 + 3 + 2)) - (( 1 + 3 + 2)))) - 2 * (( 2 + 2 + 9 * (( 1 + 3 + 2)) - (( 1 + 3 + 2)))) * 2 - 2)",
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"symbol_definitions": {
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"conditions": [],
"default_operation": " 2 + 2 + y * x - x",
"precedence": 5
},
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x + 2",
"precedence": 5
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "28c65a95-5c07-4cd1-8b57-6b2bd03ae69b"
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"question": "Define □, the rules are as follows:\non the real number field, x □ y = x - y * x * 2 - y.\nand △, the rules are as follows:\non the real number field, x △ y = 2 + 2 + y * x - x.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = y + x + 2.\nThe precedence of operations: △ = ◇ > ** > * = / = % > + = - = □。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ◇ 1 △ 9 □ 2\nPlease fill your final answer in \\boxed{}."
},
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"expression": "3 ◇ 1 △ 9 □ 2",
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"num_of_numbers": null,
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"operators": null,
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"seed": 58545156,
"simplified_expr": "( (( 2 + 2 + 9 * (( 1 + 3 + 2)) - (( 1 + 3 + 2)))) - 2 * (( 2 + 2 + 9 * (( 1 + 3 + 2)) - (( 1 + 3 + 2)))) * 2 - 2)",
"solutions_count": null,
"symbol_definitions": {
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"△": {
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"conditions": [],
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},
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x + 2",
"precedence": 5
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"target": null,
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"seed": 58545156,
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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 the sum of x and y is even, x ⊙ y = y / 5 ** x;
otherwise, x ⊙ y = abs(x) + y - x.
and ○, the rules are as follows:
when x is even, x ○ y = (5 ◎ 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: 7 ○ 3 ◎ 1 ⊙ 9
Please fill your final answer in \boxed{}. | {
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"△": null,
"▽": null,
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"operation": " (5 ◎ x ** y)"
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],
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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 * x.\nand ⊙, the rules are as follows:\nwhen the sum of x and y is even, x ⊙ y = y / 5 ** x;\notherwise, x ⊙ y = abs(x) + y - x.\nand ○, the rules are as follows:\nwhen x is even, x ○ y = (5 ◎ 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: 7 ○ 3 ◎ 1 ⊙ 9\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( (( abs((( 1 + 1 * 3))) + 9 - (( 1 + 1 * 3)))) * (( abs((( 1 + 1 * 3))) + 9 - (( 1 + 1 * 3)))) + 7)",
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"△": null,
"▽": null,
"◇": null,
"○": {
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"conditions": [
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"condition": "x是偶数",
"operation": " (5 ◎ x ** y)"
}
],
"default_operation": " y * y + x",
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},
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y + y * x",
"precedence": 5
},
"☆": null,
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"target": null,
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"seed": 38357052,
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} |
logic-v2 | 定义 ♢，规则如下：
当x大于y时，x ♢ y = y + x - y + x；
其他情况下，x ♢ y = y + x + y - 2。
和 ⊗，规则如下：
实数域上，x ⊗ y = y + y - y ♢ x。
和 ⊕，规则如下：
实数域上，x ⊕ y = (y ⊗ x - x)。
运算优先级：⊗ > ⊕ > ** > * = / = % = ♢ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ♢ 6 ⊕ 2
请将最终答案填入\boxed{}中。 | {
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"solutions_count": null,
"symbol_definitions": {
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},
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"♢": {
"associativity": "left",
"conditions": [
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"operation": " y + x - y + x"
}
],
"default_operation": " y + x + y - 2",
"precedence": 2
}
},
"target": null,
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"trace_id": "014f9ba2-86b9-4304-a4c3-94e9ae26dce5"
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"question": "定义 ♢，规则如下：\n当x大于y时，x ♢ y = y + x - y + x；\n其他情况下，x ♢ y = y + x + y - 2。\n和 ⊗，规则如下：\n实数域上，x ⊗ y = y + y - y ♢ x。\n和 ⊕，规则如下：\n实数域上，x ⊕ y = (y ⊗ x - x)。\n运算优先级：⊗ > ⊕ > ** > * = / = % = ♢ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 ♢ 6 ⊕ 2\n请将最终答案填入\\boxed{}中。"
},
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"simplified_expr": "( ((((((((6 + 6)) - (( 2 + 6 - 2 + 6))))) - 6))) + 5 - ((((((((6 + 6)) - (( 2 + 6 - 2 + 6))))) - 6))) + 5)",
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logic-v2 | Define ○, the rules are as follows:
when y is a multiple of 5, x ○ y = y + x + y;
otherwise, x ○ y = x - y - x * x.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8
Please fill your final answer in \boxed{}. | {
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},
"metadata": {
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"expression": "8",
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"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " y + x + y"
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"default_operation": " x - y - x * x",
"precedence": 1
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"♡": null,
"♢": null
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logic-v2 | 定义 ◇，规则如下：
当x等于y时，x ◇ y = 1 - 1 - y / x；
其他情况下，x ◇ y = x * y + y。
运算优先级：** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 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当x等于y时，x ◇ y = 1 - 1 - y / x；\n其他情况下，x ◇ y = x * y + y。\n运算优先级：** > * = / = % = ◇ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "10",
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"△": null,
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"◇": {
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"seed": 39779921,
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} |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y - x + x + y - y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x ⊕ y + x * x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y * x / x + 5 / 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: 5 ⊗ 5 ◎ 1 ⊕ 8
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "64.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 5 ◎ 1 ⊕ 8",
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"simplified_expr": "(((( ((((((((8 - 1)) + 1)) + 8)) - 8)) - ((((((5 * 5)) / 5)) + ((5 / 2)))) + ((((((5 * 5)) / 5)) + ((5 / 2)))) + ((((((((8 - 1)) + 1)) + 8)) - 8)) - ((((((((8 - 1)) + 1)) + 8)) - 8)))) + ((((((((5 * 5)) / 5)) + ((5 / 2)))) * ((((((5 * 5)) / 5)) + ((5 / 2))))))))",
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"conditions": [],
"default_operation": " y * x / x + 5 / 2",
"precedence": 3
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " x ⊕ y + x * x",
"precedence": 1
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "7628232f-b0ba-48ec-b20c-ea141abe79ad"
},
"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = y - x + x + y - y.\nand ◎, the rules are as follows:\non the real number field, x ◎ y = x ⊕ y + x * x.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = y * x / x + 5 / 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: 5 ⊗ 5 ◎ 1 ⊕ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "5 ⊗ 5 ◎ 1 ⊕ 8",
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"simplified_expr": "(((( ((((((((8 - 1)) + 1)) + 8)) - 8)) - ((((((5 * 5)) / 5)) + ((5 / 2)))) + ((((((5 * 5)) / 5)) + ((5 / 2)))) + ((((((((8 - 1)) + 1)) + 8)) - 8)) - ((((((((8 - 1)) + 1)) + 8)) - 8)))) + ((((((((5 * 5)) / 5)) + ((5 / 2)))) * ((((((5 * 5)) / 5)) + ((5 / 2))))))))",
"solutions_count": null,
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},
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"conditions": [],
"default_operation": " y * x / x + 5 / 2",
"precedence": 3
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
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"conditions": [],
"default_operation": " x ⊕ y + x * x",
"precedence": 1
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "7628232f-b0ba-48ec-b20c-ea141abe79ad"
},
"seed": 64841940,
"task_id": 264841940,
"task_type": "operation"
} |
logic-v2 | Define □, the rules are as follows:
when y is odd, x □ y = x - abs(x - y * 4 - y);
otherwise, x □ y = y - x * x * y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * y ** x - y + x.
The precedence of operations: ** = ⊕ > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 % 8 ⊕ 1 □ 9
Please fill your final answer in \boxed{}. | {
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},
"△": null,
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"○": null,
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"♢": null
},
"target": null,
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"trace_id": "92657472-667d-4067-bb36-82b4cfc413b0"
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"question": "Define □, the rules are as follows:\nwhen y is odd, x □ y = x - abs(x - y * 4 - y);\notherwise, x □ y = y - x * x * y.\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = 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: 1 % 8 ⊕ 1 □ 9\nPlease fill your final answer in \\boxed{}."
},
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"seed": 39280357,
"simplified_expr": "( ((1 % (( 8 * 1 ** 8 - 1 + 8)))) - abs(((1 % (( 8 * 1 ** 8 - 1 + 8)))) - 9 * 4 - 9))",
"solutions_count": null,
"symbol_definitions": {
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"operation": " x - abs(x - y * 4 - y)"
}
],
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},
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"○": null,
"◎": null,
"☆": null,
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},
"seed": 39280357,
"task_id": 239280357,
"task_type": "operation"
} |
logic-v2 | 定义 ⊗，规则如下：
当y是奇数时，x ⊗ y = y + x；
其他情况下，x ⊗ y = y * x / y + y。
和 ☆，规则如下：
实数域上，x ☆ y = x + x / y ⊗ x。
和 ▽，规则如下：
实数域上，x ▽ y = x - abs(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: 6 ** 1 ▽ 4 ☆ 1 ⊗ 10 * 1
请将最终答案填入\boxed{}中。 | {
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},
"◇": null,
"○": null,
"◎": null,
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"associativity": "left",
"conditions": [],
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"question": "定义 ⊗，规则如下：\n当y是奇数时，x ⊗ y = y + x；\n其他情况下，x ⊗ y = y * x / y + y。\n和 ☆，规则如下：\n实数域上，x ☆ y = x + x / y ⊗ x。\n和 ▽，规则如下：\n实数域上，x ▽ y = x - abs(y * 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: 6 ** 1 ▽ 4 ☆ 1 ⊗ 10 * 1\n请将最终答案填入\\boxed{}中。"
},
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},
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"○": null,
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"☆": {
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logic-v2 | Define ◎, the rules are as follows:
when y is odd, x ◎ y = x + (1) - y + x;
otherwise, x ◎ y = y * x * (y) * x.
and ♡, the rules are as follows:
when x is greater than y, x ♡ y = y ◎ x - y + x;
otherwise, x ♡ y = abs(x ** 1) * x - y.
The precedence of operations: ** = ♡ > * = / = % > + = - = ◎。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ◎ 4 / 9 ◎ 9 ♡ 6
Please 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 = y - (x - x)；
其他情况下，x ○ y = 2 * x * y + x + x。
运算优先级：** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2
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 * 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 △ 1 - 2 * 4
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 △，规则如下：
实数域上，x △ y = (x) * y - 3。
和 ◇，规则如下：
实数域上，x ◇ y = x / y △ y。
和 ♢，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 = 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 ◇ 1 - 10 ♢ 10 △ 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。
和 □，规则如下：
实数域上，x □ y = x + y + x。
和 ◇，规则如下：
当y是偶数时，x ◇ y = x * x / y；
其他情况下，x ◇ y = y - y □ x。
运算优先级：◇ > ** = □ > * = / = % > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 9 ◇ 2
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ◇，规则如下：
当y是5的倍数时，x ◇ y = x * abs(x) + y + y * 2；
其他情况下，x ◇ y = x + x + y / 5 - 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 % 5 ◇ 8
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x ** 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
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。
和 ♢，规则如下：
当y是3的倍数时，x ♢ y = x - y ** x；
其他情况下，x ♢ y = y * x * x。
和 △，规则如下：
实数域上，x △ y = x + y * y。
运算优先级：♢ > ** = ◎ = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 △ 5 ♢ 4 ◎ 10 + 2
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ♡，规则如下：
当x小于y时，x ♡ y = y / x * 3；
其他情况下，x ♡ y = x + x + (y - y)。
和 ◎，规则如下：
当y是偶数时，x ◎ y = y ♡ (x)；
其他情况下，x ◎ y = x + y / y ♡ y。
运算优先级：♡ > ◎ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ♡ 9
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ♢，规则如下：
当y是3的倍数时，x ♢ y = x + x - y * y * x；
其他情况下，x ♢ y = y + x。
和 ♡，规则如下：
实数域上，x ♡ y = y - x * y + x * y。
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 - x * 4 - 5 - 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: 7 ⊕ 2 ♢ 8 / 4 ⊕ 4 ♡ 8
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ⊙, the rules are as follows:
when x is equal to y, x ⊙ y = (x - y - y);
otherwise, x ⊙ y = (y) / x.
and △, the rules are as follows:
on the real number field, x △ y = y ** x - y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = 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 ⊙ 8
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。
和 ⊙，规则如下：
实数域上，x ⊙ y = y * x - x。
和 ♡，规则如下：
当y是奇数时，x ♡ y = x ⊙ y - y；
其他情况下，x ♡ y = abs(y) + x - y。
运算优先级：⊙ > ♢ = ♡ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♢ 5 ♡ 5 ⊙ 4
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"question": "定义 ♢，规则如下：\n实数域上，x ♢ y = y + x - x。\n和 ⊙，规则如下：\n实数域上，x ⊙ y = y * x - x。\n和 ♡，规则如下：\n当y是奇数时，x ♡ y = x ⊙ y - y；\n其他情况下，x ♡ y = abs(y) + x - y。\n运算优先级：⊙ > ♢ = ♡ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ♢ 5 ♡ 5 ⊙ 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 / 5 - x。
和 ○，规则如下：
实数域上，x ○ y = x - y - x。
和 △，规则如下：
实数域上，x △ y = x / 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: 7 △ 4 ○ 10 △ 6 ⊙ 3
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是3的倍数时，x ⊗ y = abs(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 = (x ⊗ y) + x。
和 ◇，规则如下：
实数域上，x ◇ y = 1 - 1 ◎ y - 3 + x。
运算优先级：** > * = / = % = ⊗ = ◇ > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊗ 4 ◇ 7
请将最终答案填入\boxed{}中。 | {
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},
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},
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logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y - x / (y * y).
and ⊙, the rules are as follows:
when x and y are both even, x ⊙ y = y - x * y * y;
otherwise, x ⊙ y = y - x - 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 ⊙ 4
Please fill your final answer in \boxed{}. | {
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = y - x / (y * y).\nand ⊙, the rules are as follows:\nwhen x and y are both even, x ⊙ y = y - x * y * y;\notherwise, x ⊙ y = y - x - 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 ⊙ 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 = y - abs(x * y)。
和 ◎，规则如下：
实数域上，x ◎ y = y ⊕ x。
和 ⊗，规则如下：
实数域上，x ⊗ y = (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: 1 ⊗ 4 ⊕ 1 ◎ 9 ⊗ 2
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊕，规则如下：\n实数域上，x ⊕ y = y - abs(x * y)。\n和 ◎，规则如下：\n实数域上，x ◎ y = y ⊕ x。\n和 ⊗，规则如下：\n实数域上，x ⊗ y = (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: 1 ⊗ 4 ⊕ 1 ◎ 9 ⊗ 2\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y + x + y。
和 ♡，规则如下：
当x是奇数时，x ♡ y = abs(y) * x + x；
其他情况下，x ♡ y = y ⊕ x。
和 ◎，规则如下：
当x大于y时，x ◎ y = x * y * y；
其他情况下，x ◎ y = y + abs(y + x)。
运算优先级：♡ > ** > * = / = % = ◎ > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊕ 4 ♡ 2 ◎ 9
请将最终答案填入\boxed{}中。 | {
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"operation": " abs(y) * x + x"
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logic-v2 | 定义 ◇，规则如下：
当x等于y时，x ◇ y = x - x + y；
其他情况下，x ◇ 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: 1 ◇ 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 = abs(x / y * x)。
和 ▽，规则如下：
实数域上，x ▽ y = (3 + x □ y)。
运算优先级：□ > ** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ▽ 2 □ 2 - 3
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 ** 4 * 1)。
和 ⊗，规则如下：
当x是5的倍数时，x ⊗ y = y * 1 + y / y ⊙ x；
其他情况下，x ⊗ y = y * x / x - y - (y)。
和 ▽，规则如下：
实数域上，x ▽ y = y / y * x + y * y。
运算优先级：⊙ = ⊗ > ** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 % 7 ⊙ 7 ⊗ 10 ▽ 5
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 = y - x - y；
其他情况下，x ⊙ y = x - (x) + x + y。
和 △，规则如下：
实数域上，x △ y = x - y ⊙ y * y。
和 ♢，规则如下：
当y是3的倍数时，x ♢ y = y △ x + 5；
其他情况下，x ♢ y = x + y - y + 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: 4 ⊙ 6 △ 1 % 9 ♢ 9
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logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x + y。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = x - 3 + x + y；
其他情况下，x ◎ y = 2 / x * y ♢ y * y。
和 ☆，规则如下：
实数域上，x ☆ y = x + y + 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 ☆ 9 ◎ 8
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logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x + y + x。
和 ⊗，规则如下：
当y是奇数时，x ⊗ y = y □ x + y + 3；
其他情况下，x ⊗ y = x * y。
运算优先级：□ = ⊗ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 * 5 □ 7 ⊗ 5
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ▽，规则如下：
当x大于y时，x ▽ y = y - x * (x)；
其他情况下，x ▽ y = y + x + y。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ▽ 1 * 7 + 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 / x * 2；
其他情况下，x ⊕ y = 4 + x + y。
和 ⊗，规则如下：
当x大于y时，x ⊗ y = x - y / y；
其他情况下，x ⊗ y = x ⊕ y * y。
和 ◇，规则如下：
实数域上，x ◇ y = y + x。
运算优先级：** = ⊕ > * = / = % = ⊗ = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ⊗ 8 ⊕ 8 / 10 ◇ 6
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y / x / 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: 10 △ 3
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y - y - x - y * y.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 / 5 * 2 △ 8
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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 = x + (y)。
和 ◎，规则如下：
当x和y的和是偶数时，x ◎ y = y + (y) - x；
其他情况下，x ◎ y = x ○ x - y。
运算优先级：◎ > ♢ > ** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ○ 8 ◎ 6 ♢ 5
请将最终答案填入\boxed{}中。 | {
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},
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},
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y - y + x + 2。
和 ○，规则如下：
当x小于y时，x ○ y = x * y * (y) + y；
其他情况下，x ○ y = 1 * y - y + x。
和 ▽，规则如下：
实数域上，x ▽ y = y ⊕ x。
运算优先级：▽ > ⊕ > ** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ⊕ 9 * 3 ○ 5 ▽ 6
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊕，规则如下：\n实数域上，x ⊕ y = y - y + x + 2。\n和 ○，规则如下：\n当x小于y时，x ○ y = x * y * (y) + y；\n其他情况下，x ○ y = 1 * y - y + x。\n和 ▽，规则如下：\n实数域上，x ▽ y = y ⊕ x。\n运算优先级：▽ > ⊕ > ** = ○ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 6 ⊕ 9 * 3 ○ 5 ▽ 6\n请将最终答案填入\\boxed{}中。"
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logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y - x + 3 + y.
and ○, the rules are as follows:
on the real number field, x ○ y = y ◎ y ** x + y.
The precedence of operations: ** > * = / = % = ◎ > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ○ 10
Please fill your final answer in \boxed{}. | {
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},
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"simplified_expr": "(((( ((10 ** 2)) - 10 + 3 + ((10 ** 2)))) + 10))",
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"◎": {
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"seed": 8773510,
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} |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = 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: 2 ** 6 ▽ 2
Please fill your final answer in \boxed{}. | {
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"question": "Define ▽, the rules are as follows:\non the real number field, x ▽ y = y * x + y + x / y.\nThe precedence of operations: ** = ▽ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ** 6 ▽ 2\nPlease fill your final answer in \\boxed{}."
},
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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 - 5 - 4)。
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: 2 △ 10 ** 1 ◎ 9
请将最终答案填入\boxed{}中。 | {
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"trace_id": "fecf1edb-852f-4b93-b29e-71b01dd64779"
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"question": "定义 ◎，规则如下：\n实数域上，x ◎ y = y * (y * x - 5 - 4)。\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: 2 △ 10 ** 1 ◎ 9\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "2 △ 10 ** 1 ◎ 9",
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"seed": 90286835,
"simplified_expr": "( 9 * (9 * ((((((( 2 * (2 * 10 - 5 - 4))) + 10))) ** 1)) - 5 - 4))",
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},
"seed": 90286835,
"task_id": 290286835,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y * y + y * x + y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ▽ 10
Please fill your final answer in \boxed{}. | {
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"gpt_response": "",
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"question": "Define ▽, the rules are as follows:\non the real number field, x ▽ y = y * y + y * x + y.\nThe precedence of operations: ▽ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 ▽ 10\nPlease fill your final answer in \\boxed{}."
},
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"◎": null,
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} |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = y / y / x.
and ♡, the rules are as follows:
when y is odd, x ♡ y = y / y + x;
otherwise, x ♡ y = y * abs(x / y).
and ▽, the rules are as follows:
when x is less than y, x ▽ y = (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 ⊗ 3 ▽ 5 ♡ 8
Please fill your final answer in \boxed{}. | {
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"precedence": 4
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y / y + x"
}
],
"default_operation": " y * abs(x / y)",
"precedence": 4
},
"♢": null
},
"target": null,
"total_length": null,
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"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = y / y / x.\nand ♡, the rules are as follows:\nwhen y is odd, x ♡ y = y / y + x;\notherwise, x ♡ y = y * abs(x / y).\nand ▽, the rules are as follows:\nwhen x is less than y, x ▽ y = (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: 4 ⊗ 3 ▽ 5 ♡ 8\nPlease fill your final answer in \\boxed{}."
},
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},
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"△": null,
"▽": {
"associativity": "left",
"conditions": [
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"condition": "x小于y",
"operation": " (x ⊗ y)"
}
],
"default_operation": " x + x * y",
"precedence": 4
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y / y + x"
}
],
"default_operation": " y * abs(x / y)",
"precedence": 4
},
"♢": null
},
"target": null,
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"seed": 92165294,
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logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x + abs(y - x)。
和 ◇，规则如下：
实数域上，x ◇ y = y ☆ y - x。
运算优先级：** = ◇ > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ◇ 6 ☆ 7
请将最终答案填入\boxed{}中。 | {
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"◎": null,
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"question": "定义 ☆，规则如下：\n实数域上，x ☆ y = x + abs(y - x)。\n和 ◇，规则如下：\n实数域上，x ◇ y = y ☆ y - x。\n运算优先级：** = ◇ > * = / = % > + = - = ☆。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2 ◇ 6 ☆ 7\n请将最终答案填入\\boxed{}中。"
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logic-v2 | Define ▽, the rules are as follows:
when x is even, x ▽ y = x / y * x * y;
otherwise, x ▽ y = y / x + abs(5).
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * abs(5 + x).
and □, the rules are as follows:
on the real number field, x □ y = x + 1 * x * x ▽ y.
The precedence of operations: ▽ > ** > * = / = % = □ > + = - = ⊙。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ⊙ 4 □ 4 ▽ 7
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = 4 * abs(y + x) + x - y。
和 ⊙，规则如下：
实数域上，x ⊙ y = abs(x - y * x * y ** x)。
和 ○，规则如下：
当x小于y时，x ○ y = y + y - (x + y) - y；
其他情况下，x ○ y = 2 ⊙ 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: 1 ○ 10 ⊙ 7
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ♢，规则如下：\n实数域上，x ♢ y = 4 * abs(y + x) + x - y。\n和 ⊙，规则如下：\n实数域上，x ⊙ y = abs(x - y * x * y ** x)。\n和 ○，规则如下：\n当x小于y时，x ○ y = y + y - (x + y) - y；\n其他情况下，x ○ y = 2 ⊙ 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: 1 ○ 10 ⊙ 7\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ◎，规则如下：
当y是奇数时，x ◎ y = x + y + x；
其他情况下，x ◎ y = y * x + x。
和 ○，规则如下：
实数域上，x ○ y = y * 5 + x。
运算优先级：** = ◎ > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 * 4 ◎ 4 ◎ 2 ○ 2
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 = 4 / abs(y * x)。
和 ⊗，规则如下：
实数域上，x ⊗ y = x ⊙ 1 + (y)。
和 ⊕，规则如下：
当x等于y时，x ⊕ y = 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: 1 ⊕ 4 ⊗ 1 ⊙ 1
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 odd, x ⊙ y = y - x - y;
otherwise, x ⊙ y = x + y.
and ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = x ⊙ y * x;
otherwise, 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 - 5 ⊗ 8 ○ 10 ⊙ 8
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ▽，规则如下：
当y是偶数时，x ▽ y = y + (x * 5 * 5 - x)；
其他情况下，x ▽ y = (y / 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: 1
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ☆, the rules are as follows:
when x is a multiple of 5, x ☆ y = x / 5 + y;
otherwise, x ☆ y = x ** x + y.
and □, the rules are as follows:
when x is even, x □ y = x * x ** y;
otherwise, x □ y = y ☆ (x) * y.
The precedence of operations: ☆ > ** > * = / = % > + = - = □。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ☆ 1 □ 4 / 7 / 5
Please fill your final answer in \boxed{}. | {
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"question": "Define ☆, the rules are as follows:\nwhen x is a multiple of 5, x ☆ y = x / 5 + y;\notherwise, x ☆ y = x ** x + y.\nand □, the rules are as follows:\nwhen x is even, x □ y = x * x ** y;\notherwise, x □ y = y ☆ (x) * y.\nThe precedence of operations: ☆ > ** > * = / = % > + = - = □。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ☆ 1 □ 4 / 7 / 5\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y + x + x。
和 △，规则如下：
实数域上，x △ y = x - y - x - y。
和 ◇，规则如下：
当y是5的倍数时，x ◇ y = x ** (x) + y + x；
其他情况下，x ◇ 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: 9 ◇ 9 * 6 △ 6 ⊗ 2
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = y + x + x。\n和 △，规则如下：\n实数域上，x △ y = x - y - x - y。\n和 ◇，规则如下：\n当y是5的倍数时，x ◇ y = x ** (x) + y + x；\n其他情况下，x ◇ y = y + x / x * x。\n运算优先级：** > * = / = % = ◇ > + = - = ⊗ = △。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 9 ◇ 9 * 6 △ 6 ⊗ 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 = x + y.
and ♡, the rules are as follows:
when y is a multiple of 3, x ♡ y = y * x * 1;
otherwise, x ♡ y = y * x.
The precedence of operations: ♡ > ** > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ◎ 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 and y are both odd, x ○ y = y + x;
otherwise, x ○ y = x - x + y.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 + 5 % 1 ○ 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 + x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = 1 * 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 ♢ 10
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y - x + x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y □ x.
The precedence of operations: ⊕ > ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 □ 10 ⊕ 9
Please fill your final answer in \boxed{}. | {
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"associativity": "left",
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logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y * 4 - x。
和 ▽，规则如下：
实数域上，x ▽ y = y + y - x。
运算优先级：☆ = ▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ▽ 8 ☆ 4 ☆ 2
请将最终答案填入\boxed{}中。 | {
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"simplified_expr": "( 2 * 4 - (( 4 * 4 - (( 8 + 8 - 8)))))",
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"seed": 28583710,
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} |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x / x * y。
和 ⊕，规则如下：
实数域上，x ⊕ y = y * x ☆ x。
运算优先级：⊕ > ** > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ☆ 5 ⊕ 6
请将最终答案填入\boxed{}中。 | {
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"answer": "5",
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},
"metadata": {
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"seed": 86817521,
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} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x - y * y * abs(4 * y).
and ⊗, the rules are as follows:
when x is a multiple of 5, x ⊗ y = x + y ♢ x - x * x;
otherwise, x ⊗ y = x - 2 * 1 + y.
and △, the rules are as follows:
on the real number field, x △ y = x ⊗ x * x / y + (5).
The precedence of operations: △ > ♢ > ** > * = / = % > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ♢ 2 ⊗ 5 △ 9
Please fill your final answer in \boxed{}. | {
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"◎": null,
"☆": null,
"♡": null,
"♢": {
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}
},
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},
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],
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"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
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"conditions": [],
"default_operation": " x - y * y * abs(4 * y)",
"precedence": 4
}
},
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},
"seed": 62046332,
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} |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = (x - y) - y.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 7
Please fill your final answer in \boxed{}. | {
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},
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"▽": null,
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"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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logic-v2 | 定义 ♡，规则如下：
当x大于y时，x ♡ y = x / x - x - y；
其他情况下，x ♡ y = x ** y - x + y。
和 □，规则如下：
实数域上，x □ y = (x + y) * y。
运算优先级：♡ = □ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 3
请将最终答案填入\boxed{}中。 | {
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"default_operation": " x ** y - x + y",
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"♢": null
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"question": "定义 ♡，规则如下：\n当x大于y时，x ♡ y = x / x - x - y；\n其他情况下，x ♡ y = x ** y - 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: 1 ♡ 3\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "1 ♡ 3",
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"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": 29153280,
"simplified_expr": "( 1 ** 3 - 1 + 3)",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": {
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"default_operation": " (x + y) * y",
"precedence": 4
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x大于y",
"operation": " x / x - x - y"
}
],
"default_operation": " x ** y - x + y",
"precedence": 4
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "174be3be-1c6b-4e64-9623-90e160488660"
},
"seed": 29153280,
"task_id": 229153280,
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} |
logic-v2 | Define ♢, the rules are as follows:
when y is a multiple of 3, x ♢ y = y / y + x;
otherwise, x ♢ y = x - y - x * 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: 3 / 3 ** 10 ⊕ 2 ♢ 6
Please fill your final answer in \boxed{}. | {
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"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
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"operation": " y / y + x"
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],
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}
},
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"question": "Define ♢, the rules are as follows:\nwhen y is a multiple of 3, x ♢ y = y / y + x;\notherwise, x ♢ y = x - y - x * x.\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = y * x * x * x.\nThe precedence of operations: ** > * = / = % = ⊕ > + = - = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 / 3 ** 10 ⊕ 2 ♢ 6\nPlease fill your final answer in \\boxed{}."
},
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"seed": 30778761,
"simplified_expr": "( (( 2 * ((3 / ((3 ** 10)))) * ((3 / ((3 ** 10)))) * ((3 / ((3 ** 10)))))) - 6 - (( 2 * ((3 / ((3 ** 10)))) * ((3 / ((3 ** 10)))) * ((3 / ((3 ** 10)))))) * (( 2 * ((3 / ((3 ** 10)))) * ((3 / ((3 ** 10)))) * ((3 / ((3 ** 10)))))))",
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"♡": null,
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"seed": 30778761,
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logic-v2 | Define ♡, the rules are as follows:
when x is odd, x ♡ y = y * x / 4;
otherwise, x ♡ y = 3 + y * x - 4.
and △, the rules are as follows:
when x is a multiple of 5, x △ y = 2 - x ♡ y - x - y;
otherwise, x △ y = y - y * y + y + x.
The precedence of operations: △ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ♡ 3 ** 8 △ 7
Please fill your final answer in \boxed{}. | {
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"condition": "x是奇数",
"operation": " y * x / 4"
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"default_operation": " 3 + y * x - 4",
"precedence": 1
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"♢": null
},
"target": null,
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"question": "Define ♡, the rules are as follows:\nwhen x is odd, x ♡ y = y * x / 4;\notherwise, x ♡ y = 3 + y * x - 4.\nand △, the rules are as follows:\nwhen x is a multiple of 5, x △ y = 2 - x ♡ y - x - y;\notherwise, x △ y = y - y * y + y + x.\nThe precedence of operations: △ > ** > * = / = % > + = - = ♡。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ♡ 3 ** 8 △ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 3 ** 8 △ 7",
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"seed": 76797708,
"simplified_expr": "( 3 + ((3 ** (( 7 - 7 * 7 + 7 + 8)))) * 2 - 4)",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
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"△": {
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"operation": " 2 - x ♡ y - x - y"
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"precedence": 5
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x是奇数",
"operation": " y * x / 4"
}
],
"default_operation": " 3 + y * x - 4",
"precedence": 1
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "4b5edbaf-b5dd-496a-9e4c-3fdaf851f6f3"
},
"seed": 76797708,
"task_id": 276797708,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
when x is less than y, x ◇ y = y + x - 4 ** 2;
otherwise, x ◇ y = 5 * y + 1 + x.
and □, the rules are as follows:
when the sum of x and y is odd, x □ y = (x) + y ◇ y;
otherwise, x □ y = 2 + y / x * 2.
and ☆, 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: 2 □ 10 ◇ 10 ☆ 9
Please fill your final answer in \boxed{}. | {
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"solutions_count": null,
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},
"○": null,
"◎": null,
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"conditions": [],
"default_operation": " x + x * y / y",
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},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
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"question": "Define ◇, the rules are as follows:\nwhen x is less than y, x ◇ y = y + x - 4 ** 2;\notherwise, x ◇ y = 5 * y + 1 + x.\nand □, the rules are as follows:\nwhen the sum of x and y is odd, x □ y = (x) + y ◇ y;\notherwise, x □ y = 2 + y / x * 2.\nand ☆, 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: 2 □ 10 ◇ 10 ☆ 9\nPlease fill your final answer in \\boxed{}."
},
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"expression": "2 □ 10 ◇ 10 ☆ 9",
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"seed": 25410427,
"simplified_expr": "( 5 * (( 10 + 10 * 9 / 9)) + 1 + (( 2 + 10 / 2 * 2)))",
"solutions_count": null,
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"operation": " (x) + y ◇ y"
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},
"△": null,
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"◇": {
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"conditions": [
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"condition": "x小于y",
"operation": " y + x - 4 ** 2"
}
],
"default_operation": " 5 * y + 1 + x",
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},
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x + x * y / y",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
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},
"seed": 25410427,
"task_id": 225410427,
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} |
logic-v2 | Define ○, the rules are as follows:
when y is odd, x ○ y = y / y + y * y * x;
otherwise, x ○ y = (x - 3 * y).
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 - 6 * 6 ○ 6
Please fill your final answer in \boxed{}. | {
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"symbol_definitions": {
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"◎": null,
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"♡": null,
"♢": null
},
"target": null,
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"trace_id": "cfc44908-fc91-4c45-a13e-4600e24914c7"
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"question": "Define ○, the rules are as follows:\nwhen y is odd, x ○ y = y / y + y * y * x;\notherwise, x ○ 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: 6 - 6 * 6 ○ 6\nPlease fill your final answer in \\boxed{}."
},
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"expression": "6 - 6 * 6 ○ 6",
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"solutions_count": null,
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"⊗": null,
"⊙": null,
"□": null,
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"▽": null,
"◇": null,
"○": {
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"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"seed": 84818466,
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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x和y都是偶数时，x ⊕ y = x - 5 ♢ 4 * y + y；
其他情况下，x ⊕ y = x * (x) + y / x。
和 △，规则如下：
实数域上，x △ y = y / 2 - y / x + x。
运算优先级：** = ♢ > * = / = % = ⊕ = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 7 ⊕ 2 ♢ 4
请将最终答案填入\boxed{}中。 | {
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"○": null,
"◎": null,
"☆": null,
"♡": null,
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},
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"question": "定义 ♢，规则如下：\n实数域上，x ♢ y = y ** x / x - y。\n和 ⊕，规则如下：\n当x和y都是偶数时，x ⊕ y = x - 5 ♢ 4 * y + y；\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 = y / 2 - y / x + x。\n运算优先级：** = ♢ > * = / = % = ⊕ = △ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 △ 7 ⊕ 2 ♢ 4\n请将最终答案填入\\boxed{}中。"
},
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"○": null,
"◎": null,
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logic-v2 | 定义 ♡，规则如下：
当x大于y时，x ♡ y = (x * x) - y；
其他情况下，x ♡ y = y + x * y + x。
和 □，规则如下：
当y是奇数时，x □ y = (y * x) + x；
其他情况下，x □ y = y + x ♡ y + y。
运算优先级：♡ > ** > * = / = % > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 □ 3
请将最终答案填入\boxed{}中。 | {
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"♢": null
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"question": "定义 ♡，规则如下：\n当x大于y时，x ♡ y = (x * x) - y；\n其他情况下，x ♡ y = y + x * y + x。\n和 □，规则如下：\n当y是奇数时，x □ y = (y * x) + x；\n其他情况下，x □ y = y + x ♡ y + y。\n运算优先级：♡ > ** > * = / = % > + = - = □。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 □ 3\n请将最终答案填入\\boxed{}中。"
},
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"operation": " (x * x) - y"
}
],
"default_operation": " y + x * y + x",
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},
"♢": null
},
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logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = x + y ** 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 % 3 ▽ 6 / 2
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = 3 - x - y - y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x + (1) - y * y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x + y ⊙ x - y.
The precedence of operations: ** = ☆ > * = / = % > + = - = ⊙ = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ⊙ 7 ☆ 6
Please fill your final answer in \boxed{}. | {
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"precedence": 1
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"○": null,
"◎": null,
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"associativity": "left",
"conditions": [],
"default_operation": " x + y ⊙ x - y",
"precedence": 3
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"♡": null,
"♢": null
},
"target": null,
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"question": "Define ⊙, the rules are as follows:\non the real number field, x ⊙ y = 3 - x - y - y.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = x + (1) - y * y.\nand ☆, the rules are as follows:\non the real number field, x ☆ y = x + y ⊙ x - y.\nThe precedence of operations: ** = ☆ > * = / = % > + = - = ⊙ = ▽。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ⊙ 7 ☆ 6\nPlease fill your final answer in \\boxed{}."
},
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"expression": "4 ⊙ 7 ☆ 6",
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"simplified_expr": "( 3 - 4 - ((((( 3 - ((7 + 6)) - 7 - 7)) - 6))) - ((((( 3 - ((7 + 6)) - 7 - 7)) - 6))))",
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},
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y ⊙ x - y",
"precedence": 3
},
"♡": null,
"♢": null
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"target": null,
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"trace_id": "afa598da-50da-4081-8f23-7bc721ec04cc"
},
"seed": 54942873,
"task_id": 254942873,
"task_type": "operation"
} |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x - y + x。
和 ⊙，规则如下：
实数域上，x ⊙ y = x * x ♢ y。
和 ⊗，规则如下：
当x和y都是奇数时，x ⊗ y = (y) - x * 4；
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: 1 / 10 ♢ 8 ⊗ 7 ⊙ 4
请将最终答案填入\boxed{}中。 | {
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"○": null,
"◎": null,
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"question": "定义 ♢，规则如下：\n实数域上，x ♢ y = x - y + x。\n和 ⊙，规则如下：\n实数域上，x ⊙ y = x * x ♢ y。\n和 ⊗，规则如下：\n当x和y都是奇数时，x ⊗ y = (y) - x * 4；\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: 1 / 10 ♢ 8 ⊗ 7 ⊙ 4\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "1 / 10 ♢ 8 ⊗ 7 ⊙ 4",
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"seed": 50029288,
"simplified_expr": "(((( ((1 / ((((10 - 8)) + 10)))) - ((1 / ((((10 - 8)) + 10)))) + ((1 / ((((10 - 8)) + 10)))))) / ((7 * ((((7 - 4)) + 7))))))",
"solutions_count": null,
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"⊙": {
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"conditions": [],
"default_operation": " x * x ♢ y",
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},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
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"default_operation": " x - y + x",
"precedence": 5
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"target": null,
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"seed": 50029288,
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} |
logic-v2 | Define ⊗, the rules are as follows:
when y is a multiple of 5, x ⊗ y = abs(y * y * x) - x;
otherwise, x ⊗ y = x / y * y * x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = abs(x * y * y) + x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y ⊕ x - 4.
The precedence of operations: ** > * = / = % = ◎ > + = - = ⊗ = ⊕。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ⊕ 2 ⊗ 4 ◎ 5
Please fill your final answer in \boxed{}. | {
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"operation": " abs(y * y * x) - x"
}
],
"default_operation": " x / y * y * x",
"precedence": 1
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y ⊕ x - 4",
"precedence": 2
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"question": "Define ⊗, the rules are as follows:\nwhen y is a multiple of 5, x ⊗ y = abs(y * y * x) - x;\notherwise, x ⊗ y = x / y * y * x.\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = abs(x * y * y) + x.\nand ◎, the rules are as follows:\non the real number field, x ◎ y = y ⊕ 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: 5 ⊕ 2 ⊗ 4 ◎ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "5 ⊕ 2 ⊗ 4 ◎ 5",
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"simplified_expr": "( (( abs(5 * 2 * 2) + 5)) / ((((( abs(5 * 4 * 4) + 5)) - 4))) * ((((( abs(5 * 4 * 4) + 5)) - 4))) * (( abs(5 * 2 * 2) + 5)))",
"solutions_count": null,
"symbol_definitions": {
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},
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"conditions": [
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"operation": " abs(y * y * x) - x"
}
],
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},
"⊙": null,
"□": null,
"△": null,
"▽": null,
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"conditions": [],
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},
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"♡": null,
"♢": null
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"seed": 76658864,
"task_id": 276658864,
"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 / 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: 2 □ 10 ◎ 1 ◎ 8
Please fill your final answer in \boxed{}. | {
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"target": null,
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},
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"simplified_expr": "( (( ((( (10 * 1))) * 8))) / (( ((( (10 * 1))) * 8))) / 2 + 1)",
"solutions_count": null,
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},
"seed": 62474634,
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"task_type": "operation"
} |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y + 5 / y - x * y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x - 5 * y.
The precedence of operations: ** > * = / = % = ♡ > + = - = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ☆ 7 ♡ 7
Please fill your final answer in \boxed{}. | {
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"conditions": [],
"default_operation": " y + 5 / y - x * y",
"precedence": 2
},
"♢": null
},
"target": null,
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"trace_id": "21b2de12-54ab-4231-aff0-60916ad5f949"
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"question": "Define ♡, the rules are as follows:\non the real number field, x ♡ y = y + 5 / y - x * y.\nand ☆, the rules are as follows:\non the real number field, x ☆ y = x - 5 * y.\nThe precedence of operations: ** > * = / = % = ♡ > + = - = ☆。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 ☆ 7 ♡ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "10 ☆ 7 ♡ 7",
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logic-v2 | 定义 ♡，规则如下：
当y是5的倍数时，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 - 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 ♡ 4 ◇ 9 ♡ 3
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 + 5 + 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 + y * y。
和 ♡，规则如下：
当y是偶数时，x ♡ y = x ⊕ x + (y) / x；
其他情况下，x ♡ y = y + x * y * y。
运算优先级：□ > ** > * = / = % = ♡ > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ⊕ 3 ♡ 5 □ 8
请将最终答案填入\boxed{}中。 | {
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