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 + y + x + y。
和 ○，规则如下：
当x是3的倍数时，x ○ y = y * 1 + x；
其他情况下，x ○ 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: 6 ▽ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ♡，规则如下：
当y是偶数时，x ♡ y = x + abs(y) / 3；
其他情况下，x ♡ y = y * x * x。
和 ⊗，规则如下：
实数域上，x ⊗ y = x * y。
运算优先级：** > * = / = % > + = - = ♡ = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 * 1 ⊗ 8 ♡ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "576",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 * 1 ⊗ 8 ♡ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ⊗, the rules are as follows:
when x is less than y, x ⊗ y = x * y;
otherwise, x ⊗ y = y * x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x * x - y.
and ♡, the rules are as follows:
when x is even, x ♡ y = y + x * y;
otherwise, x ♡ y = x - 2 + y.
The precedence of operations: ♢ > ... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 6 ⊗ 1 ♢ 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 5, x ☆ y = y - x * y;
otherwise, x ☆ y = x - x - y.
and ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = y + x / x;
otherwise, x ⊗ y = y * y - x.
The precedence of operations: ⊗ > ** = ☆ > * = / = % > + = -。
Parentheses have the highest p... | {
"game_data": {
"answer": "-396",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 7 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define △, the rules are as follows:
when x is equal to y, x △ y = y - x - x;
otherwise, 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: 7... | {
"game_data": {
"answer": "2.529412",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 % 9 △ 8 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 ⊕，规则如下：
当x等于y时，x ⊕ y = x - y + (y - 2)；
其他情况下，x ⊕ y = y - x / y + y ** 2。
和 ⊗，规则如下：
实数域上，x ⊗ y = 1 * 5 ** 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: 10 ☆ 2 + 5 ⊗ 6 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-593.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 2 + 5 ⊗ 6 ⊕ 5",
"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 = 3 * y * y ** x.
and □, the rules are as follows:
on the real number field, x □ y = x - 5 - y ⊙ y.
and ⊗, the rules are as follows:
when y is a multiple of 3, x ⊗ y = abs(x * x * x + y);
otherwise, x ⊗ y = y * x + y - x.
The precedence of oper... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 2 ⊙ 9 ⊗ 8",
"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5的倍数时，x ☆ y = x + y + x + x；
其他情况下，x ☆ y = x + y + x - x。
和 △，规则如下：
实数域上，x △ y = y - 1 ☆ x * 2。
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: 2 * 3 ♢ 7 △ 7 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-21.012803",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 * 3 ♢ 7 △ 7 ☆ 2",
"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 less than y, x □ y = x + y;
otherwise, x □ y = abs(x / y + y) + y.
and ⊕, the rules are as follows:
when y is odd, x ⊕ y = y ** x □ y;
otherwise, x ⊕ y = 4 * 5 * x - y.
The precedence of operations: ** = □ > * = / = % > + = - = ⊕。
Parentheses have the highest priori... | {
"game_data": {
"answer": "159.491166",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊕ 9 / 9 □ 6 □ 8",
"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：
实数域上，x ♢ y = y - x * 4 - y。
运算优先级：** > * = / = % > + = - = ☆ = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♢ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 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 = x - y - x。
和 ◎，规则如下：
当y是5的倍数时，x ◎ y = 1 + x ☆ (y * x)；
其他情况下，x ◎ y = y * 4 - 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 ◎ 1 / 7 ☆ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 1 / 7 ☆ 3",
"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 - 4 - y.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 % 4 ▽ 3
Please fill your... | {
"game_data": {
"answer": "-2.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 % 4 ▽ 3",
"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 - x + y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + (y * x ♢ x + y).
and ○, the rules are as follows:
when the sum of x and y is odd, x ○ y = y / 5 ** y ⊕ x;
otherwise, x ○ y = abs(y * y * y + y ** x).
Th... | {
"game_data": {
"answer": "-42",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 10 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ○，规则如下：
当x等于y时，x ○ y = x ** y；
其他情况下，x ○ y = 3 - x + 3 / y。
运算优先级：** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ○ 10 * 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-42.3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 10 * 9",
"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 - y + 5.
and ♡, the rules are as follows:
when y is a multiple of 3, x ♡ y = y * x - x;
otherwise, x ♡ y = x ⊗ y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * x * 3.
The precedence of operations: ** = ⊙ > * = /... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 7 * 1 ⊙ 7 ⊗ 5",
"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 a multiple of 5, x ♢ y = x + (y - x + y) ** x;
otherwise, x ♢ y = y / x + y * y * y.
and ⊗, the rules are as follows:
when x is odd, x ⊗ y = y / x * 5 - y - x;
otherwise, x ⊗ y = x / x / y / x - y.
and ○, the rules are as follows:
on the real number field, x ○ y = ... | {
"game_data": {
"answer": "-738.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 3 ⊗ 1 ♢ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y * x + y - x * x.
and ○, the rules are as follows:
on the real number field, x ○ y = 4 * y + x.
The precedence of operations: ○ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "-299.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 9 □ 8 / 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ⊗, the rules are as follows:
when the sum of x and y is even, x ⊗ y = x * 1 - 3 * (2 ** y);
otherwise, x ⊗ y = 4 + x + (x - y) / y.
and ⊕, the rules are as follows:
when x is greater than y, x ⊕ y = y * x * 1 * 1;
otherwise, x ⊕ y = 5 / x - 4 ⊗ y.
and ◎, the rules are as follows:
when the sum of x and y ... | {
"game_data": {
"answer": "2.625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 10 ⊗ 4 % 8 ◎ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ○，规则如下：
当x和y都是奇数时，x ○ y = x + y + x；
其他情况下，x ○ y = x * y / x。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 - 10 ○ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 - 10 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ⊗, the rules are as follows:
when x is even, x ⊗ y = x * x - y;
otherwise, x ⊗ y = x - y + (y).
and ○, the rules are as follows:
on the real number field, x ○ y = abs(y) + x + x.
and □, the rules are as follows:
on the real number field, x □ y = y * x * x.
The precedence of operations: ○ > ** = □ > * = /... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 7 ○ 6 □ 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 = y * y * y + x + x.
and ◇, the rules are as follows:
when x is greater than y, x ◇ y = y ◎ x - y - 2 + y;
otherwise, x ◇ y = x * y ◎ x.
The precedence of operations: ** > * = / = % > + = - = ◎ = ◇。
Parentheses have the highest priority, and the ... | {
"game_data": {
"answer": "1619",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 8 * 4 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y + abs(x).
and ⊙, the rules are as follows:
when x and y are both even, x ⊙ y = y - x * x;
otherwise, x ⊙ y = y - x + y.
The precedence of operations: ** = □ > * = / = % = ⊙ > + = -。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 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:
on the real number field, x ⊙ y = y * x + x + 1.
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 calcula... | {
"game_data": {
"answer": "121",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 * 6 ⊙ 9 ☆ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ♢，规则如下：
当y是奇数时，x ♢ y = x / 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 = (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 ♡ 3 ♢ 8 ◇ 4 % 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.210526",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 3 ♢ 8 ◇ 4 % 10",
"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 = x * y + y + y.
and △, the rules are as follows:
on the real number field, x △ y = y + x + y * y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y * 4 - (x - 1).
The precedence of operations: △ > ☆ > ** > * = / = % = ♢ > + = ... | {
"game_data": {
"answer": "-76",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 8 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y - x + x / 4 + x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = 1 / x * x * y + x.
and □, the rules are as follows:
on the real number field, x □ y = y / x + x ♢ y * x.
The precedence of operations: □ > ** > * = / = % > + ... | {
"game_data": {
"answer": "12.09375",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 7 ⊕ 9 ♢ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ◇, the rules are as follows:
when x is equal to y, x ◇ y = y + x / y + y;
otherwise, x ◇ y = abs(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 ex... | {
"game_data": {
"answer": "110",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 2 * 5",
"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 equal to y, x ⊕ y = abs(y + x) - y;
otherwise, x ⊕ y = abs(x - y - x * 2).
and ▽, the rules are as follows:
on the real number field, x ▽ y = 2 - abs(y + x) - x.
and ♢, the rules are as follows:
when x is greater than y, x ♢ y = 5 + x * y;
otherwise, x ♢ y = y ⊕ x... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 3 ⊕ 6 + 4 ♢ 10 * 8",
"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 / 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 △ 4 ** 1
Please fill you... | {
"game_data": {
"answer": "2402",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 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x等于y时，x ☆ y = x + x + y * x + y；
其他情况下，x ☆ y = 3 + y - y / y / x。
和 □，规则如下：
实数域上，x □ y = x - y ☆ x。
运算优先级：□ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 □ 9 * 2 ☆ 5 ☆ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6.875079",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 9 * 2 ☆ 5 ☆ 4",
"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 * 2.
and ♡, the rules are as follows:
when the sum of x and y is even, x ♡ y = x - y * x;
otherwise, x ♡ y = x ◎ y.
The precedence of operations: ♡ > ** > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "4.066667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 4 + 10 ♡ 7",
"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。
运算优先级：** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 * 10 ▽ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "45",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 * 10 ▽ 5",
"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 * abs(y * y).
and ☆, the rules are as follows:
when x is even, x ☆ y = x * y + 4;
otherwise, x ☆ y = x * y - y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x + y * x.
The precedence of operations: ▽ > ** = ☆ > * = / =... | {
"game_data": {
"answer": "1764",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 5 ▽ 1 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x - y / y * x + y.
and ⊗, the rules are as follows:
when x and y are both odd, x ⊗ y = y + y - x ⊕ y + y;
otherwise, x ⊗ y = (x ⊕ y) * y / y + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x + x - x ** y.
The precedenc... | {
"game_data": {
"answer": "-723",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊕ 7 ⊕ 3 ◎ 1 ⊗ 3",
"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).
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 ☆ 9
Please fill your final ... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 * 3 ☆ 9",
"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 = 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 ○ 3 - 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1.888889",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 3 - 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y是5的倍数时，x ⊙ y = y + y + x；
其他情况下，x ⊙ y = x * y * x。
和 ▽，规则如下：
当y是奇数时，x ▽ y = y - x ⊙ 1 * y；
其他情况下，x ▽ y = y - x / x + y。
和 ◎，规则如下：
实数域上，x ◎ y = x + y - 1 - x。
运算优先级：** = ⊙ > * = / = % = ▽ = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◎ 1 ⊙ 5 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 1 ⊙ 5 ▽ 2",
"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 = 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: 6 + 9 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 + 9 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ♢, the rules are as follows:
when x is greater than y, x ♢ y = y / x * y / x;
otherwise, x ♢ y = 5 * x - y - 2.
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 - y - x) ♢ x.
The precedence of operations: ♢... | {
"game_data": {
"answer": "-32",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 5 ♡ 5 ♢ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ○, the rules are as follows:
when y is a multiple of 5, x ○ y = y * x + 1;
otherwise, x ○ y = x + y * y.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression... | {
"game_data": {
"answer": "361",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 3 ** 2",
"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 = 1 - 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: 5 ○ 2 ** 1 % 7
Please f... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 2 ** 1 % 7",
"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是偶数时，x ⊙ y = y + x * (x + x)；
其他情况下，x ⊙ y = y - y / y + x。
和 ♡，规则如下：
当x大于y时，x ♡ y = y * x / x * y；
其他情况下，x ♡ y = y + x * y + 4。
和 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = x - x - x * y；
其他情况下，x ⊕ y = 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 ⊙ 10 ⊕ 9 ♡ 2
请将最终答案... | {
"game_data": {
"answer": "-1470",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊙ 10 ⊕ 9 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = 3 + x - x * y。
和 ◎，规则如下：
实数域上，x ◎ y = (y - x) / x - y。
运算优先级：◎ > ** > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♡ 5 + 6 ◎ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-18.166667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 5 + 6 ◎ 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 * y * x) ** 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 ♡ 1 □ 6 □ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "34",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 1 □ 6 □ 3",
"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 = abs(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: 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：
当x和y都是奇数时，x □ y = y - y + x / 1；
其他情况下，x □ y = y - y + y / x。
和 △，规则如下：
实数域上，x △ y = y □ x / y + y。
运算优先级：△ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 □ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 □，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 = (x - y / x) + x。
和 △，规则如下：
实数域上，x △ y = y - y - x。
和 ◇，规则如下：
实数域上，x ◇ y = (y / x - 4 / x)。
运算优先级：△ > ** > * = / = % = □ = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ◇ 1 □ 1 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2.833333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 1 □ 1 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define ⊕, the rules are as follows:
when the sum of x and y is odd, x ⊕ y = 1 * x - y - x;
otherwise, x ⊕ y = x + y - 5.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y * x - 3.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y - y + x * x.
The precedence of operations: ⊕... | {
"game_data": {
"answer": "397",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 9 ⊕ 8 ◇ 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 / y - x / y。
和 ◎，规则如下：
当x是5的倍数时，x ◎ y = x + y + 2 / x；
其他情况下，x ◎ y = 2 + 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "59",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 4",
"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 = 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
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：
当x是5的倍数时，x ◇ y = x ** x * y；
其他情况下，x ◇ y = y ** x ** x。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ** 8 - 2 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5936",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ** 8 - 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：
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: 4 ◇ 9 + 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 9 + 4",
"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 = y + x + 4。
和 ☆，规则如下：
当x小于y时，x ☆ y = y - y / x；
其他情况下，x ☆ y = x + x ♡ y * x。
运算优先级：** = ♡ > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 3 ♡ 6 ☆ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "468",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 3 ♡ 6 ☆ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x - y * x.
and ♢, the rules are as follows:
when x is less than y, x ♢ y = y + x - x;
otherwise, x ♢ y = x + (x + y).
and ◎, the rules are as follows:
on the real number field, x ◎ y = x + y - 3.
The precedence of operations: ** = ♢ > * = / =... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 6 ♢ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y - x * x - x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y + (5 + y * x).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y + x + x + y.
The precedence of operations: ▽ > ** = ♢ = ⊕ > * = / = % > + = ... | {
"game_data": {
"answer": "-4063",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 5 ♢ 3 ⊕ 5 ▽ 4 ⊕ 6",
"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 less than y, x ◎ y = x - 1 + y;
otherwise, x ◎ y = 5 - y - x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x ◎ x - y * y.
and ♡, the rules are as follows:
when x is even, x ♡ y = x + y - y * y;
otherwise, x ♡ y = x - x + x * y.
The precedence... | {
"game_data": {
"answer": "-63",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 7 ♡ 2 ◎ 2",
"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 * y + y - (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: 7 - 3 ○ 2 ♡ 2 / 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 - 3 ○ 2 ♡ 2 / 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
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是奇数时，x ○ y = x * y ♡ x - x；
其他情况下，x ○ y = x - (5 / y + x)。
运算优先级：** = ♡ > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ○ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.555556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 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 = y + abs(x + x)。
和 ⊙，规则如下：
实数域上，x ⊙ y = y / x * y。
和 ○，规则如下：
当x是5的倍数时，x ○ y = 1 ** 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: 3 - 6 ⊙ 5 ⊗ 8 ** 7 ○ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "132.599296",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 - 6 ⊙ 5 ⊗ 8 ** 7 ○ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": nul... |
logic-v2 | Define ☆, the rules are as follows:
when x and y are both even, x ☆ y = abs(y + x - y);
otherwise, x ☆ y = y / y + y + y * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - y + y / x + y.
The precedence of operations: ⊙ > ** > * = / = % > + = - = ☆。
Parentheses have the highest priority, a... | {
"game_data": {
"answer": "44.285714",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 1 ☆ 7 ⊙ 10 + 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 □，规则如下：
当x是3的倍数时，x □ y = y + y / y + x * y；
其他情况下，x □ y = x - x ** y / (y * y)。
和 ⊕，规则如下：
实数域上，x ⊕ y = 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: 9 ⊕ 5 - 3 □ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-25.444444",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 5 - 3 □ 4",
"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 = x + x + x - y.
and ⊙, the rules are as follows:
when the sum of x and y is even, x ⊙ y = x ♡ y - y + x;
otherwise, x ⊙ y = x / y + y.
The precedence of operations: ⊙ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the e... | {
"game_data": {
"answer": "-1.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊙ 9 / 2 ♡ 1",
"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。
和 ◇，规则如下：
实数域上，x ◇ y = x - y * x。
运算优先级：♡ > ** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ♡ 3 ◇ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-36",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 3 ◇ 3",
"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 = 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 ▽ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 4",
"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 * x - x - y ** x.
and ○, the rules are as follows:
when y is a multiple of 3, x ○ y = 5 ◎ (5 + y) * x;
otherwise, x ○ y = y - 5 + 1 + x - 3.
The precedence of operations: ** > * = / = % > + = - = ◎ = ○。
Parentheses have the highest priority, ... | {
"game_data": {
"answer": "14.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 4 ◎ 2 + 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ♢, the rules are as follows:
when x is equal to y, x ♢ y = abs(y * x ** y) - x + y;
otherwise, x ♢ y = x - x - y * x - y.
and ◇, the rules are as follows:
when x is greater than y, x ◇ y = x ♢ y * x + y;
otherwise, x ◇ y = x * 4 + x + 1 ♢ y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ ... | {
"game_data": {
"answer": "636",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 3 ♢ 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:
on the real number field, x ♢ y = y - 2 * abs(x).
and ⊙, the rules are as follows:
when x is even, x ⊙ y = x + x - y;
otherwise, x ⊙ y = x + x + y.
and ◇, the rules are as follows:
when x is even, x ◇ y = x + (y) + 2;
otherwise, x ◇ y = x ** y + x.
The precedence of operati... | {
"game_data": {
"answer": "-64",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 10 ◇ 5 ♢ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ⊕, the rules are as follows:
when x is a multiple of 5, x ⊕ y = abs(y * x - x);
otherwise, x ⊕ y = x * y - y.
and ⊙, 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 = (x + y * x).
The precedence of operations: ⊕ = ♡ > ** ... | {
"game_data": {
"answer": "96",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 2 ⊙ 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是奇数时，x □ y = y + x - 3；
其他情况下，x □ y = y + x - y。
和 ◎，规则如下：
当x是5的倍数时，x ◎ y = y + x - x；
其他情况下，x ◎ y = x / x / x □ y。
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: 5 ⊙ 5 ◎ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 5 ◎ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ○, the rules are as follows:
when y is a multiple of 3, x ○ y = y + 2 / x - y;
otherwise, x ○ y = (x * y).
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expressi... | {
"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是3的倍数时，x ◇ y = x + abs(1 + y + 4 / y)；
其他情况下，x ◇ y = y + x * (y + 3 + 3)。
运算优先级：** = ◇ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 * 1 / 3 ◇ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 * 1 / 3 ◇ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ♢, the rules are as follows:
when x is greater than y, x ♢ y = 1 + 5 * y - x;
otherwise, x ♢ y = x / 2 + x + y.
and ♡, the rules are as follows:
when y is odd, x ♡ y = x ♢ y;
otherwise, x ♡ y = abs(x + x * 1 + y).
and ◇, the rules are as follows:
on the real number field, x ◇ y = x + x - y.
The precede... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 8 ◇ 6",
"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是3的倍数时，x ⊙ y = abs(y * x) + y；
其他情况下，x ⊙ y = (x + y - x)。
和 ♢，规则如下：
当x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：
当x和y都是奇数时，x □ y = x ** y + 4；
其他情况下，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: 6 + 4 + 4 ⊙ 6 □ 5 ♢ 3
请将最终答案填入\boxe... | {
"game_data": {
"answer": "-15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 + 4 + 4 ⊙ 6 □ 5 ♢ 3",
"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 less than y, x ○ y = x / y - x - y - y;
otherwise, 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 th... | {
"game_data": {
"answer": "9.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 - 6 - 2 ○ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ♢, the rules are as follows:
when x is greater than y, x ♢ y = x + x - y;
otherwise, x ♢ y = x + y - x * x.
and □, the rules are as follows:
when x is even, x □ y = x ♢ y + x * x;
otherwise, x □ y = x + y + x.
and ⊗, the rules are as follows:
when x is equal to y, x ⊗ y = x + y + y ♢ y;
otherwise, x ⊗ ... | {
"game_data": {
"answer": "35",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 2 □ 7 ♢ 7",
"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是偶数时，x ◇ y = y * x * 2 * 4 - y；
其他情况下，x ◇ y = 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: 9 ◇ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "284",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ☆，规则如下：
当x和y都是奇数时，x ☆ y = x + abs(y / y)；
其他情况下，x ☆ y = y + x。
和 △，规则如下：
实数域上，x △ y = abs(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 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 4",
"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 + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x + x + y.
and ▽, the rules are as follows:
when x is even, x ▽ y = x + y;
otherwise, x ▽ y = (y * y) ◎ x.
The precedence of operations: ◎ > ** > * = / = % > + = - ... | {
"game_data": {
"answer": "41",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 2 + 2 ♢ 8 ▽ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = (x * y - 2).
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 calculate... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 2 ♡ 10 ♡ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ♡, the rules are as follows:
when x is even, x ♡ y = x - y * x;
otherwise, x ♡ y = y * 3 / x.
and ☆, the rules are as follows:
when y is even, x ☆ y = y * y - x;
otherwise, x ☆ y = y / y * x.
The precedence of operations: ♡ > ** = ☆ > * = / = % > + = -。
Parentheses have the highest priority, and the expr... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 7 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 □，规则如下：
当x和y的和是偶数时，x □ y = x - 1 + y * x；
其他情况下，x □ y = x + y + y * 5。
和 ⊕，规则如下：
当y是偶数时，x ⊕ y = x □ (y) - x；
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 □ 3 ⊕ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "49",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 3 ⊕ 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:
when x and y are both even, x ⊙ y = x + abs(x) * y;
otherwise, 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 = y + x + (y).
The precedence of operations: ♢ > △ ... | {
"game_data": {
"answer": "150",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊙ 4 △ 10",
"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 = y - x + 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: 3 ◎ 10 * 5 % 5 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 10 * 5 % 5 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * x + y + 1.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x * x * y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y * (y / y) ♢ x.
The precedence of operations: ** = ⊕ > * = / = % = ♢ = ▽ > + = -。
P... | {
"game_data": {
"answer": "38416",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 8 ♢ 4 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define □, the rules are as follows:
when x is a multiple of 5, x □ y = 5 * x - y;
otherwise, 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 insi... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 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 = 5 + y - 2 / x；
其他情况下，x ⊗ y = x * 1 * y / x。
和 ♡，规则如下：
实数域上，x ♡ y = x ⊗ y * y + 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: 7 ◇ 5 ⊗ 5 ♡ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◇ 5 ⊗ 5 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 △，规则如下：
当y是3的倍数时，x △ y = abs(y - x) - y + 5；
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: 7 * 5 △ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "70",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 * 5 △ 2",
"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 - x * x。
运算优先级：** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ▽ 3 * 4 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-71025.261257",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 3 * 4 ▽ 3",
"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 = 2 - x * y.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9
Please fill your final answer... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"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和y都是奇数时，x ▽ y = x * x / y + x / y；
其他情况下，x ▽ y = x + 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: 3 * 8 % 1 ▽ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 * 8 % 1 ▽ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ▽，规则如下：
当x是偶数时，x ▽ y = x * y * x / x；
其他情况下，x ▽ y = x - 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: 10 ▽ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "60",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 6",
"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 = x * (y) + y + x。
和 △，规则如下：
实数域上，x △ y = (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: 6 □ 5 △ 2 □ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.937799",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 5 △ 2 □ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define ◇, the rules are as follows:
when x is equal to y, x ◇ y = y * y ** x;
otherwise, x ◇ y = (x + y) + y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: ... | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 5 + 8 / 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◇，规则如下：
当x和y都是奇数时，x ◇ y = y * 5 + x；
其他情况下，x ◇ y = y + x - 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: 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"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 y is a multiple of 3, x ☆ y = y - (y) + x;
otherwise, x ☆ y = y * abs(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 expressi... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 2",
"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 + 3 + x。
和 ♡，规则如下：
当y是偶数时，x ♡ y = 5 ♢ x * y；
其他情况下，x ♡ y = y ♢ x + y。
运算优先级：♢ > ** > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ♡ 4 ♢ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "32",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 4 ♢ 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：
当x是3的倍数时，x ♢ y = y * 5 - y + x / x；
其他情况下，x ♢ y = x / y / x - 2 * x。
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 = 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: 1 ♢ 7 ♡ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 7 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ♡，规则如下：
当x和y的和是奇数时，x ♡ y = y + y / x * abs(x)；
其他情况下，x ♡ y = x / x + y。
和 ♢，规则如下：
当x大于y时，x ♢ y = y / y - y * x；
其他情况下，x ♢ 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: 2 ♢ 2 ♡ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 2 ♡ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ♡, the rules are as follows:
when y is odd, x ♡ y = x - (x ** y - 2);
otherwise, x ♡ y = x * y * x / x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 3 + y + 5 ♡ x.
The precedence of operations: ** = ♡ > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression i... | {
"game_data": {
"answer": "2.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 / 2 ♡ 4 ◇ 7 % 3",
"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 = y - (x - x).
and ♡, the rules are as follows:
on the real number field, x ♡ y = (x + x - y) ** x.
and ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = y * (x □ x) + y;
otherwise, x ◎ y = x - y * x - 2.
The precedence of op... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 / 2 * 8 ◎ 5 □ 2 ♡ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
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