env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x - (2 * y) - 2。
和 △，规则如下：
当x和y的和是奇数时，x △ y = (x + y □ y) - x；
其他情况下，x △ y = (y * y - x)。
运算优先级：** = □ > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 △ 4 □ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 4 □ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = 5 * 5 + y + x.
and □, the rules are as follows:
on the real number field, x □ y = y ⊙ x - y - y - x.
and ◇, the rules are as follows:
when x is a multiple of 5, x ◇ y = 5 + x □ x ** y;
otherwise, x ◇ y = 5 * (x) - 4 ⊙ y.
The precedence of ope... | {
"game_data": {
"answer": "109",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 7 ⊙ 8 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x - x + 2 - y。
和 ▽，规则如下：
实数域上，x ▽ y = (x * y ◎ x + y)。
运算优先级：** = ◎ > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-41",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
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 + y) - x.
The precedence of operations: ◎ = □ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calcula... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ◎，规则如下：
当y是5的倍数时，x ◎ y = abs(y) + x；
其他情况下，x ◎ y = y * (y) * x。
和 ♢，规则如下：
当x和y的和是偶数时，x ♢ y = x * y；
其他情况下，x ♢ y = (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: 6 ♢ 6 ◎ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "576",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 6 ◎ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 △，规则如下：
当y是奇数时，x △ y = 5 - y ** x + 2 - x；
其他情况下，x △ y = x * x * y * 3 + 1。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◎, the rules are as follows:
when x and y are both odd, x ◎ y = x + y;
otherwise, x ◎ y = 5 * y * 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 p... | {
"game_data": {
"answer": "630",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 9 ◎ 9 / 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x * y - 3.
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 = y * x - x.
The precedence of operations: ◇ > ** > * = / = % > + = - = ♢ = ▽。
Parentheses... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 10 ♢ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = x * y - y / y;
otherwise, x ◇ y = y + y + y + x.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ex... | {
"game_data": {
"answer": "4.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 10 ◇ 2 / 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ○, the rules are as follows:
when the sum of x and y is odd, x ○ y = y + x * y;
otherwise, x ○ y = y ** x / y * y.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = (x / 3) * y.
and ♢, the rules are as follows:
when y is a multiple of 5, x ♢ y = (y * x);
otherwise, x ♢ y = x ◎ x + y.
The precedence of operations: ♢ > ** > * = / = % > + = - = ◎。
Parentheses have the highest priority, and the expression insi... | {
"game_data": {
"answer": "9.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x + 3 + y + y。
和 ⊙，规则如下：
实数域上，x ⊙ y = y + (x + x / 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: 8 ◎ 8 ⊙ 2 % 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 8 ⊙ 2 % 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x + 4 / y / x。
和 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = y * x + y □ x；
其他情况下，x ⊕ y = x + x * y - x + y。
运算优先级：□ > ** = ⊕ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ⊕ 4 □ 8 / 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4.5375",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 4 □ 8 / 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * (y + x) - y - x.
and ⊗, the rules are as follows:
when the sum of x and y is even, x ⊗ y = y + x - 2;
otherwise, x ⊗ y = (y + x + y).
and ○, the rules are as follows:
when x and y are both odd, x ○ y = x + (x - y / x ⊕ x);
otherwise, x ○ ... | {
"game_data": {
"answer": "1.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 3 ○ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 △，规则如下：
当x是偶数时，x △ y = (3) + x + y * x + y；
其他情况下，x △ y = 4 + 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: 9 - 10 △ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 - 10 △ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = abs(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: 7 △ 8 % 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 8 % 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
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: 7
Please fill your fin... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ○, the rules are as follows:
when x and y are both even, x ○ y = y + x + x + x;
otherwise, x ○ y = x / y * y ** 3.
and ▽, the rules are as follows:
when y is even, x ▽ y = x + y + 3 - 4;
otherwise, x ▽ y = x ○ y.
and △, the rules are as follows:
when x and y are both even, x △ y = y * x;
otherwise, x △... | {
"game_data": {
"answer": "64512.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 10 ▽ 3 ○ 4 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y / x + x * y + y。
和 ♢，规则如下：
当x等于y时，x ♢ y = y - x ⊕ y - x - x；
其他情况下，x ♢ y = y - y + x / y - x。
和 △，规则如下：
当x等于y时，x △ y = 4 ** x ♢ y；
其他情况下，x △ y = 5 ♢ y / x + x。
运算优先级：** = ⊕ > * = / = % = △ > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 % 6 △ 10 ♢ 7 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.982456",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 % 6 △ 10 ♢ 7 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = x - y * y;
otherwise, x ⊗ y = y + y * x + x.
and ♡, the rules are as follows:
when x is odd, x ♡ y = y + y * x - x;
otherwise, x ♡ y = x + y.
and ○, the rules are as follows:
on the real number field, x ○ y = y + 5 ⊗ x.
The precedence of op... | {
"game_data": {
"answer": "1833",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 5 ♡ 7 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = (y * y - x + y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = (y) - y * x.
The precedence of operations: ** = ▽ > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "-18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y / x。
和 ◎，规则如下：
当x大于y时，x ◎ y = (y * y) - x * x；
其他情况下，x ◎ y = abs(x) * y。
和 △，规则如下：
当x大于y时，x △ y = y - 1 ◎ x * y；
其他情况下，x △ y = y + y ◎ y + (x)。
运算优先级：** > * = / = % = ⊗ = ◎ > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ⊗ 5 △ 9 ◎ 4 ⊗ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.092367",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 5 △ 9 ◎ 4 ⊗ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ◎, the rules are as follows:
when x is even, x ◎ y = (3 - x) * y * y;
otherwise, x ◎ y = 1 * y - y - x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = 1 / x * y + 1.
The precedence of operations: ◎ > ⊕ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression i... | {
"game_data": {
"answer": "-9.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 6 ◎ 1 - 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 □，规则如下：
当x是奇数时，x □ y = x + x + y * y；
其他情况下，x □ y = x + y - y / y。
和 ▽，规则如下：
实数域上，x ▽ y = y * y □ x + y。
运算优先级：□ > ** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 □ 3 ▽ 5 ▽ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "486",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 3 ▽ 5 ▽ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y - y - y + x - x。
和 ▽，规则如下：
实数域上，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: 5 □ 4 ▽ 3 % 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 4 ▽ 3 % 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 △，规则如下：
当x是5的倍数时，x △ y = abs(x + x + y)；
其他情况下，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: 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
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: 10 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1e-05",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = x - (y - x * 2)。
和 ▽，规则如下：
实数域上，x ▽ y = y + y * y * x。
和 △，规则如下：
当x和y的和是奇数时，x △ y = y ⊙ y + x；
其他情况下，x △ y = 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: 1 ⊙ 6 △ 7 ▽ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1149",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 6 △ 7 ▽ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y * 4 / x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 3
Please fill your final an... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 □，规则如下：
当x和y都是偶数时，x □ y = x + 5 + y + 3；
其他情况下，x □ y = x * y + x - y - y。
和 ⊗，规则如下：
当x和y都是奇数时，x ⊗ y = y * x + x + x；
其他情况下，x ⊗ y = 3 + 3 ** x - 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: 10 ⊗ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "59047",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊗ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
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 less than y, x △ y = y ♡ x - y - (y);
otherwise, x △ y = y ♡ (x - y + y).
The precedence of operations: ♡ > △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the exp... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 + 4 ♡ 4 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ☆, the rules are as follows:
when x is a multiple of 3, x ☆ y = 2 + y * x - x;
otherwise, x ☆ y = y * y + x + 3.
and ⊕, the rules are as follows:
when x is less than y, x ⊕ y = 2 - y ☆ 3 - x;
otherwise, x ⊕ y = x ☆ y + 3.
The precedence of operations: ⊕ > ☆ > ** > * = / = % > + = -。
Parentheses have the ... | {
"game_data": {
"answer": "-10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 5 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 △，规则如下：
当x和y都是偶数时，x △ y = y * x - y；
其他情况下，x △ y = x * 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: 10 △ 10 * 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "720",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 10 * 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * x + x.
and ☆, the rules are as follows:
when x is less than y, x ☆ y = y * x + y;
otherwise, x ☆ y = x + y ⊙ x.
and ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = y - x / y;
otherwise, x ◎ y = 1 + y ☆ x.
The preced... | {
"game_data": {
"answer": "198.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 3 ◎ 7 ☆ 6 ☆ 9 - 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ◇, the rules are as follows:
when x is a multiple of 3, 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 expressio... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ◇，规则如下：
当x等于y时，x ◇ y = y ** 5 / 1 ** x / 4；
其他情况下，x ◇ y = 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 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "154",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 6 ◇ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y + x - x.
and □, the rules are as follows:
when the sum of x and y is even, x □ y = y - x - y;
otherwise, x □ y = (y * x).
and △, the rules are as follows:
when y is a multiple of 5, x △ y = x ♢ 5 * y;
otherwise, x △ y = y ** y * x.
The pr... | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 9 △ 3 ♢ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x - y - y.
and ♢, the rules are as follows:
when x is odd, x ♢ y = x - y + y;
otherwise, x ♢ y = abs(x * x * y).
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x - y ** x.
The precedence of operations: ⊗ > ** > * = / = % =... | {
"game_data": {
"answer": "640.002441",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 6 ⊙ 1 ⊙ 4 ♢ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x / 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: 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = 4 * y + x + x。
和 ☆，规则如下：
实数域上，x ☆ y = abs(x - y ** y) - x。
和 ◎，规则如下：
当x是3的倍数时，x ◎ y = (y ♡ x) * x / x；
其他情况下，x ◎ y = y - y * x。
运算优先级：♡ = ◎ > ☆ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ♡ 9 ☆ 2 ◎ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.037037",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 9 ☆ 2 ◎ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = abs(1 ** y) + x * x。
和 ▽，规则如下：
当x和y都是偶数时，x ▽ y = y - y / (y □ x)；
其他情况下，x ▽ y = 2 + 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 □ 2 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "17502",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 2 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ⊙，规则如下：
当x等于y时，x ⊙ y = x + x * 1 - y；
其他情况下，x ⊙ y = x / y * y。
和 ◇，规则如下：
实数域上，x ◇ y = x - x + x ⊙ y * y。
和 □，规则如下：
实数域上，x □ y = y ◇ x * x - y - y。
运算优先级：◇ > ** > * = / = % = □ > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊙ 6 □ 3 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 6 □ 3 ◇ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ▽, the rules are as follows:
when x is equal to y, x ▽ y = y - 4 * x ** y + x;
otherwise, x ▽ y = 3 - 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 th... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y + x - y.
and ○, the rules are as follows:
on the real number field, x ○ y = x + y ⊙ y.
and ◇, the rules are as follows:
when the sum of x and y is even, x ◇ y = x + x * y;
otherwise, x ◇ y = x ⊙ 5 + y.
The precedence of operations: ○ > ◇ > ... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 6 ⊙ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ◇，规则如下：
当x小于y时，x ◇ y = x * x * x / x + y；
其他情况下，x ◇ y = x - x * x / abs(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 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "34",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ♡, the rules are as follows:
when x is greater than y, x ♡ y = abs(x * x * y);
otherwise, x ♡ y = x - 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 - (y) - x.
The precedence of operations: ○ > ** =... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 5 ⊕ 4 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ⊕，规则如下：
当y是奇数时，x ⊕ y = x * y - x + y；
其他情况下，x ⊕ y = x / y * 2。
和 ◇，规则如下：
实数域上，x ◇ y = y * y + x / x。
和 ○，规则如下：
实数域上，x ○ y = y - y - 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 ◇ 2 ⊕ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 2 ⊕ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ▽，规则如下：
实数域上，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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y * y - x - 3。
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 = abs(x - y + y)。
运算优先级：♢ > ** = ☆ > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ☆ 10 △ 8 - 2 ♢ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "95.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 10 △ 8 - 2 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
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 * y + x)。
和 △，规则如下：
实数域上，x △ y = y + x * 2。
运算优先级：** > * = / = % = △ > + = - = ⊗ = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ▽ 7 ⊗ 4 △ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "952",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 7 ⊗ 4 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x - y - 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 ◇ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ◇, the rules are as follows:
when x is equal to y, x ◇ y = y ** x * x;
otherwise, x ◇ y = y + (x + x + y).
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expressi... | {
"game_data": {
"answer": "64",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 9 + 3 ◇ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x / y + abs(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: 2 ♡ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.285714",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y - (x) / 4 + 2 * x。
和 ♡，规则如下：
当y是偶数时，x ♡ y = x □ y * y + x；
其他情况下，x ♡ y = x * x □ y - y。
运算优先级：** = ♡ > * = / = % = □ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 + 3 □ 5 ♡ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "204.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 + 3 □ 5 ♡ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = 2 + x + y - 4 / x。
和 ♢，规则如下：
当x是偶数时，x ♢ y = (4 - y ☆ y - x)；
其他情况下，x ♢ y = y - x + x ☆ y - y。
运算优先级：** = ☆ = ♢ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ☆ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x + y * y.
and △, the rules are as follows:
when x is odd, x △ y = x - x + y;
otherwise, x △ y = y * x ▽ x.
The precedence of operations: ▽ > ** = △ > * = / = % > + = -... | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 2 ⊗ 7 % 5 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ◇, the rules are as follows:
when x is odd, x ◇ y = (y * y * y + x) - x;
otherwise, x ◇ y = y + x - y.
The precedence of operations: ** > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: ... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 5 % 4 * 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = x + y / abs(2 * 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: 6 / 7 ▽ 10 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.857143",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 / 7 ▽ 10 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 ▽，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: 1 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ♡, 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 ♡ 4 * y.
The precedence of operations: ♡ = ⊙ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "759",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊙ 9 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define □, the rules are as follows:
when x is greater than y, x □ y = x - y + y + (y);
otherwise, x □ y = (y) * x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x - x + y + x □ y.
The precedence of operations: □ > ** > * = / = % = ♢ > + = -。
Parentheses have the highest priority, and the expr... | {
"game_data": {
"answer": "-90",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 2 □ 7 ♢ 9 * 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | 定义 △，规则如下：
当x小于y时，x △ y = 3 + 1 + x / x * y；
其他情况下，x △ y = y ** 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: 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y + x。
和 ▽，规则如下：
实数域上，x ▽ y = (x * 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 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y * y * x + y。
和 □，规则如下：
实数域上，x □ y = abs(y * 1 - y ** x)。
运算优先级：◎ = □ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 % 8 ◎ 5 □ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 % 8 ◎ 5 □ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
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:
on the real number field, x ○ y = abs(x * 5) + y / 1.
and □, the rules are as follows:
on the real number field, x □ y = (y) * 4 / x * 4.
The precedence of operations: △ = ○ = □ > ** > * = / = % ... | {
"game_data": {
"answer": "-0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 4 △ 2 □ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ☆，规则如下：
当x是奇数时，x ☆ y = y - y * x；
其他情况下，x ☆ y = x * y * x * y + y。
和 ◎，规则如下：
实数域上，x ◎ y = x * 1 + y ** 1 / x。
和 ♡，规则如下：
当x是奇数时，x ♡ y = y - 4 ** 4 + y + x；
其他情况下，x ♡ y = y * x * (y ◎ x * y)。
运算优先级：♡ > ** = ☆ > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ☆ 7 - 6 ♡ 4 ◎ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1531.005225",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 7 - 6 ♡ 4 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
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: 3 ▽ 6
Please fill your final an... | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = 3 ** x * y.
and △, the rules are as follows:
when the sum of x and y is even, x △ y = y ⊗ x * y;
otherwise, x △ y = y - x / x.
and ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = y - x - y;
otherwise, x ◇ y = y △ y / x.
The ... | {
"game_data": {
"answer": "0.355556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 5 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
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。
和 ☆，规则如下：
实数域上，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 ⊙ 2 * 7 ☆ 2 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 2 * 7 ☆ 2 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ◎，规则如下：
当x是3的倍数时，x ◎ y = x ** 5 + 5 + y / 1；
其他情况下，x ◎ y = x + y + x + 4。
和 ▽，规则如下：
实数域上，x ▽ y = 3 * x ◎ y + 1 * x。
和 ◇，规则如下：
当x是奇数时，x ◇ y = x + y + x ◎ 2 + 3；
其他情况下，x ◇ y = abs(x + y / 3) * y。
运算优先级：◎ > ** = ◇ > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◎ 3 ▽ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "203",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 3 ▽ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x - x * 5 - y + x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = (x ** y) - 1 □ 1.
The precedence of operations: ** > * = / = % = ♢ > + = - = □。
Parentheses have the highest priority, and the expression inside the parentheses... | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊗, the rules are as follows:
when y is a multiple of 3, x ⊗ y = y / x + 5;
otherwise, x ⊗ y = y * abs(x) + 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 even, x ☆ y = y + x / x;
otherwise, x ☆ y = (y - x) + y.
The precedence... | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 10 ☆ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x ** y + x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8
Please fill your final answe... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x / y - x。
和 ⊕，规则如下：
当x是奇数时，x ⊕ y = x - y ⊗ y；
其他情况下，x ⊕ y = y * x。
和 ☆，规则如下：
当x是5的倍数时，x ☆ y = y + x；
其他情况下，x ☆ y = x ** (x ** y)。
运算优先级：⊕ > ** > * = / = % = ⊗ > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ☆ 9 ⊗ 3 - 8 % 8 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6.999661",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 9 ⊗ 3 - 8 % 8 ⊕ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,... |
logic-v2 | 定义 ☆，规则如下：
当x等于y时，x ☆ y = x - x * y + 5；
其他情况下，x ☆ y = x + x + x + y。
和 ♢，规则如下：
实数域上，x ♢ y = x - 3 ☆ 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 ☆ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 9 ☆ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x * 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: 6 △ 5
Please fill your ... | {
"game_data": {
"answer": "1291",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth... |
logic-v2 | 定义 ▽，规则如下：
当x是偶数时，x ▽ y = (x + y)；
其他情况下，x ▽ y = (x + x + y)。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = 4 - (x) / y * x。
和 ○，规则如下：
实数域上，x ○ y = y / y ** x / x ☆ x。
运算优先级：** = ☆ > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ○ 6 % 1 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 6 % 1 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = 5 + abs(x) + y + x。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ▽, 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: 4 % 1 ▽ 8
Please fill your ... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 % 1 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = x - x + y。
和 ◇，规则如下：
实数域上，x ◇ y = x / 3 * y。
和 △，规则如下：
实数域上，x △ y = x ⊙ x + y。
运算优先级：◇ = △ > ** = ⊙ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◇ 9 ⊙ 2 △ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 9 ⊙ 2 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ◎, 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 * y ◎ y.
The precedence of operations: ** = ◎ > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "18920",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 5 ◎ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ▽, the rules are as follows:
when y is even, x ▽ y = y - 3 - (x - x) / y;
otherwise, x ▽ y = 2 + y * x - 3 + 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 exp... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y + (x * y - x).
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 % 1 △ 1 / 3
Please fill... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 % 1 △ 1 / 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x * y + y / x。
和 ◇，规则如下：
当x小于y时，x ◇ y = x / y - x ◎ x；
其他情况下，x ◇ y = y / (2 + x)。
运算优先级：** > * = / = % = ◎ = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "64.285714",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = 4 * 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ♢, the rules are as follows:
when x is equal to y, x ♢ y = x * x + y;
otherwise, x ♢ y = y * x * y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x ♢ y / x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y / (3 ♢ x).
The precedence of operations: ⊕ > ♢ > ** > * = ... | {
"game_data": {
"answer": "3675",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 9 ⊕ 7 ♢ 3 ♢ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define △, the rules are as follows:
when x is greater than y, x △ y = x * y * y;
otherwise, x △ y = (x / y) / x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expressio... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ♢, the rules are as follows:
when x is less than y, x ♢ y = x ** x - y;
otherwise, x ♢ y = y + x * y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + y ♢ x.
The precedence of operations: ** > * = / = % > + = - = ♢ = ⊙。
Parentheses have the highest priority, and the expression inside ... | {
"game_data": {
"answer": "180",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth... |
logic-v2 | Define ♡, the rules are as follows:
when x and y are both even, x ♡ y = x * y + y + y - x;
otherwise, x ♡ y = x + 4 + 3 - 5 + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x - y + 1 * 5 ♡ y.
The precedence of operations: ◎ > ** > * = / = % = ♡ > + = -。
Parentheses have the highest priority... | {
"game_data": {
"answer": "4.692308",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 / 6 ◎ 1 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x * (y - y * y) + y.
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ▽ 4
Please fill you... | {
"game_data": {
"answer": "-44",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ▽，规则如下：
当y是5的倍数时，x ▽ y = y + abs(x) * x；
其他情况下，x ▽ y = (y + y * x - x)。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "50",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
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: 8 △ 7 / 8
Please fill your fina... | {
"game_data": {
"answer": "2.875",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 7 / 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ▽, the rules are as follows:
when x and y are both odd, x ▽ y = abs(y + 1 + 2 - x * 4);
otherwise, x ▽ y = y - 5 - x / 3.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y + x + y * y - x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y ** x ▽ x - x.
The precedence... | {
"game_data": {
"answer": "116.444444",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 2 ▽ 7 ◇ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = (y * y * x / x)。
和 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = x - y + y ◎ x ** x；
其他情况下，x ⊕ y = x * x * y + y * x。
运算优先级：⊕ > ** = ◎ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◎ 9 ⊕ 1 * 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "56700",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 9 ⊕ 1 * 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y / x - y.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ◇ 3 ** 8 ◇ 5
Please fill your... | {
"game_data": {
"answer": "-4.998045",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 3 ** 8 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y * x + x.
and ♢, the rules are as follows:
when x is greater than y, x ♢ y = y + x;
otherwise, x ♢ y = y / y - x.
The precedence of operations: ** = ♢ > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression inside th... | {
"game_data": {
"answer": "36",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 3 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ○，规则如下：
当y是偶数时，x ○ y = (x + y) * x；
其他情况下，x ○ y = (y + y - x)。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ○ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y + (y) - x + 5。
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 - y。
运算优先级：** = ⊗ > * = / = % > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊗ 7 □ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 7 □ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y - x + y - 2。
和 ▽，规则如下：
当x和y都是偶数时，x ▽ y = 2 / 2 + y ☆ x；
其他情况下，x ▽ y = x * y + x ☆ y。
运算优先级：☆ > ** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ☆ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth... |
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