env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ◇，规则如下：
当x是偶数时，x ◇ y = y - x * x；
其他情况下，x ◇ y = x - y * x。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-63",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 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：
实数域上，x ◇ y = x * y * x。
运算优先级：** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7
请将最终答案填入\boxed{}中。 | {
"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 | 定义 ▽，规则如下：
实数域上，x ▽ y = y + y * (x + x)。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ▽ 9 % 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 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 the sum of x and y is even, x ○ y = x - abs(y + x);
otherwise, x ○ y = x * y.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the exp... | {
"game_data": {
"answer": "630",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 10 ○ 7",
"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 y is a multiple of 5, x ◎ y = x * y ** x;
otherwise, x ◎ y = x + y - y.
and ⊕, the rules are as follows:
when x is equal to y, x ⊕ y = x ◎ y * 3;
otherwise, x ⊕ y = y + x * x.
The precedence of operations: ** = ◎ > * = / = % = ⊕ > + = -。
Parentheses have the highest prio... | {
"game_data": {
"answer": "33",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 8",
"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3的倍数时，x ○ y = y / y + x + x；
其他情况下，x ○ y = (x - y - y) * x。
运算优先级：** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": nu... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * x + 2.
and ♡, the rules are as follows:
when x is a multiple of 3, x ♡ y = y + 4 * x;
otherwise, x ♡ y = y ⊕ x + x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x ⊕ y.
The precedence of operations: ♡ = ◎ > ** > * = /... | {
"game_data": {
"answer": "12440",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 5 ◎ 3 ♡ 7 ◎ 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 = y ** x - x + y + x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 1 / 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 1 / 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 x is less than y, x ☆ y = y + x - y - y + x;
otherwise, x ☆ y = y * y ** x / y - y.
and ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = x + y * y - y ☆ y;
otherwise, x ⊗ y = 1 + y * 3 / 5 ☆ x.
and ⊙, the rules are as follows:
when y is odd, x ⊙ y = y ⊗ 1... | {
"game_data": {
"answer": "-228",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 5 ⊙ 2 ☆ 8",
"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 / (3 - x ** 3).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y * (x + x).
The precedence of operations: ⊗ > ** = ☆ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is ca... | {
"game_data": {
"answer": "42",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 7",
"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 = x + y ** y。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": nu... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * x + 4 + y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (y) / 5 * x / x.
and □, the rules are as follows:
on the real number field, x □ y = x - y * (y ** x).
The precedence of operations: ** = ⊙ > * = / = % = ☆ = □ > +... | {
"game_data": {
"answer": "10.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 + 8 □ 9 ⊙ 6 ☆ 3",
"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 = x / y.
and △, the rules are as follows:
on the real number field, x △ y = y * x + y.
and □, the rules are as follows:
on the real number field, x □ y = x * x ♢ y.
The precedence of operations: ** = ♢ = △ = □ > * = / = % > + = -。
Parentheses hav... | {
"game_data": {
"answer": "2.142857",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 7 △ 3 / 3 □ 3",
"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的和是偶数时，x ⊕ y = y - y / x + 5；
其他情况下，x ⊕ y = x - y - y - x。
和 ○，规则如下：
实数域上，x ○ y = x * x + y * y。
和 ☆，规则如下：
实数域上，x ☆ y = 2 / y ○ x - y。
运算优先级：○ = ☆ > ** = ⊕ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ⊕ 2 ☆ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19.961538",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 2 ☆ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ⊕，规则如下：
当x和y都是奇数时，x ⊕ y = y + x；
其他情况下，x ⊕ y = x - x - y。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = x ⊕ x * y；
其他情况下，x ◎ y = x ⊕ x + y。
和 ▽，规则如下：
实数域上，x ▽ y = y - y / x。
运算优先级：** > * = / = % = ▽ > + = - = ⊕ = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◎ 6 ▽ 1 ⊕ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 6 ▽ 1 ⊕ 4",
"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 = 2 / x - x - y * x.
and ○, the rules are as follows:
when the sum of x and y is even, x ○ y = y / x ♢ y * y * y;
otherwise, x ○ y = x + (y) + x.
and ⊕, the rules are as follows:
when x is even, x ⊕ y = abs(x - y) + x;
otherwise, x ⊕ y = y - ... | {
"game_data": {
"answer": "-311.192095",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 8 ○ 8 ⊕ 2",
"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 / x - y.
and ◇, the rules are as follows:
when y is odd, x ◇ y = x + x * y - y * x;
otherwise, x ◇ y = x * 3 + 2 - y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = (y - x * y) + 1.
The precedence of operations: ... | {
"game_data": {
"answer": "-256",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 9 ◇ 10 ⊕ 5",
"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和y都是奇数时，x ◇ y = x * x + y；
其他情况下，x ◇ y = x + (y * y)。
运算优先级：** = ◇ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ◇ 7 ◇ 8 - 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "88",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 7 ◇ 8 - 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 = 4 + y + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (x + y + x).
and ☆, the rules are as follows:
when y is odd, x ☆ y = x / x ♢ y;
otherwise, x ☆ y = x * x * y.
The precedence of operations: ♢ = ⊗ > ** > * = / = % >... | {
"game_data": {
"answer": "2880",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 4 ☆ 6 ⊗ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ♡，规则如下：
当y是奇数时，x ♡ y = y * 5 - x + (x) + x；
其他情况下，x ♡ y = x - y * 2 - 1 - y。
和 ○，规则如下：
当x是3的倍数时，x ○ y = x - abs(x / y + y)；
其他情况下，x ○ y = x - y + y。
运算优先级：♡ > ** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ○ 8 ** 3 ♡ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 8 ** 3 ♡ 5",
"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 = x + y - x * x * y；
其他情况下，x ☆ y = y * x * y - y / y。
和 ⊗，规则如下：
实数域上，x ⊗ y = y - 3 - x + y ☆ y。
运算优先级：⊗ > ☆ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ⊗ 10 * 1 ☆ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "63126",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 10 * 1 ☆ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x - y * x + x.
and △, the rules are as follows:
on the real number field, x △ y = (x - y) - y * 3.
and ○, the rules are as follows:
on the real number field, x ○ y = y - x * x.
The precedence of operations: △ > ** > * = / = % = ⊗ > + = - = ○。
P... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 3 + 1 ○ 1 △ 8 % 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ⊕, the rules are as follows:
when y is odd, x ⊕ y = y - x + y;
otherwise, x ⊕ y = (y * x).
and ◎, the rules are as follows:
on the real number field, x ◎ y = y + x + y * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y ⊕ x - x + x.
The precedence of operations: ⊕ > ◎ = ⊙ > ** > * =... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 4 ⊕ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y ** y * x / x.
The precedence of operations: ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 □ 1
Please fill your fin... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 1",
"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是奇数时，x ♡ y = x * y + x / 4；
其他情况下，x ♡ y = y + x * x。
和 ☆，规则如下：
实数域上，x ☆ y = x * y * x。
运算优先级：☆ > ** > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♡ 8 ☆ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "272",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 8 ☆ 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：
实数域上，x ♡ y = x / x * y。
和 △，规则如下：
实数域上，x △ y = x ** y + y。
运算优先级：** = ♡ > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ♡ 8 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4100",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 8 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ⊕, the rules are as follows:
when y is a multiple of 3, x ⊕ y = abs(x ** x) - x - y * y;
otherwise, x ⊕ y = x - (x) - y / x.
and ☆, the rules are as follows:
when y is odd, x ☆ y = y ⊕ (y - 4) + x;
otherwise, x ☆ y = 1 + x + y - 3 * 1.
and ▽, the rules are as follows:
on the real number field, x ▽ y = ... | {
"game_data": {
"answer": "704.444444",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 10 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | Define ◎, the rules are as follows:
when x is odd, x ◎ y = x * x + y - y;
otherwise, x ◎ y = (y + x) + 5 - x.
and □, the rules are as follows:
on the real number field, x □ y = x - y + 3 - x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y - x + y □ y.
The precedence of operations: □ > ** =... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 5 ◎ 2",
"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 ** 2 - x。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"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 odd, x ▽ y = 2 - y / x + y * 1;
otherwise, x ▽ y = y * (x / y + 4) - y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expr... | {
"game_data": {
"answer": "9.111111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 8",
"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 y is a multiple of 3, x □ y = x + y;
otherwise, x □ y = 3 + y + x.
The precedence of operations: □ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ... | {
"game_data": {
"answer": "5",
"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_dept... |
logic-v2 | Define ▽, the rules are as follows:
when x and y are both even, x ▽ y = x * y + x;
otherwise, x ▽ y = x + x ** y.
and ◎, the rules are as follows:
when y is even, x ◎ y = x + y * x;
otherwise, x ◎ y = y * x + x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x - y * x.
The precedence of op... | {
"game_data": {
"answer": "-840",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 8 ◎ 1 ▽ 6",
"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 - x) - y + 2.
and ○, the rules are as follows:
when the sum of x and y is even, x ○ y = x ♡ y;
otherwise, x ○ y = y * x - y + x.
The precedence of operations: ○ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the exp... | {
"game_data": {
"answer": "-3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 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：
当x是3的倍数时，x ⊙ y = y * x + y；
其他情况下，x ⊙ y = (x + y + y + x)。
和 ▽，规则如下：
实数域上，x ▽ y = abs(x - 5 - y / x)。
和 ♢，规则如下：
实数域上，x ♢ y = y * x * y。
运算优先级：▽ > ** = ⊙ = ♢ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ♢ 9 ♢ 2 ▽ 9 ⊙ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "63803.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 9 ♢ 2 ▽ 9 ⊙ 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 = x - y * y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x - y ⊕ x.
and △, the rules are as follows:
on the real number field, x △ y = x + y * y.
The precedence of operations: ⊕ = ⊙ > ** > * = / = % = △ > + = -。
Parentheses... | {
"game_data": {
"answer": "203",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 5 △ 4 ⊙ 8 ⊕ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y * x - 4。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 10",
"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 odd, x ◇ y = x * y + y * x;
otherwise, x ◇ y = x - y * x * x - y.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression... | {
"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小于y时，x ♢ y = abs(y + x)；
其他情况下，x ♢ y = y - x * x。
和 ⊗，规则如下：
实数域上，x ⊗ y = y ♢ y / x。
和 ⊕，规则如下：
实数域上，x ⊕ y = y - 4 ♢ x。
运算优先级：♢ > ** > * = / = % = ⊗ > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊕ 8 ⊕ 8 ♢ 6 ⊗ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-26.793103",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 8 ⊕ 8 ♢ 6 ⊗ 4",
"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 = y + x * (x - x)。
和 □，规则如下：
当x小于y时，x □ y = y * x - (y - y * 2)；
其他情况下，x □ y = 4 + 1 ♡ x - y * 5。
运算优先级：□ > ** = ♡ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 4 ♡ 9 ** 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 4 ♡ 9 ** 1",
"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 = x + 3 + y - x + 4；
其他情况下，x ☆ y = (x) + x * 1 - y。
和 □，规则如下：
当x和y都是奇数时，x □ y = 4 - 5 ☆ y * 2 / x；
其他情况下，x □ y = 2 * y ☆ x + x * 2。
运算优先级：** = □ > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 * 9 □ 10 ☆ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "330",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 * 9 □ 10 ☆ 10",
"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 = y - 5 * x；
其他情况下，x □ y = y + x + x + x。
和 ☆，规则如下：
当x和y的和是奇数时，x ☆ y = y □ y * x；
其他情况下，x ☆ y = y □ 5 * x - y。
运算优先级：** > * = / = % = ☆ > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 * 7 ☆ 10 □ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "698",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 * 7 ☆ 10 □ 8",
"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 = 5 + x + y * y - x.
and △, the rules are as follows:
when x and y are both even, x △ y = y - x + y - x * 3;
otherwise, x △ y = 5 ☆ y * x + 5.
The precedence of operations: ☆ > ** > * = / = % > + = - = △。
Parentheses have the highest priority, an... | {
"game_data": {
"answer": "75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 3",
"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 = x + x / y + y.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ○ 10 % 6
Please fill your... | {
"game_data": {
"answer": "2.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 10 % 6",
"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 a multiple of 5, x ♢ y = (y + 3 * 1 * x);
otherwise, x ♢ y = 5 * 1 * y - x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y / x * y * 4.
and ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = x + (y + x * y) ♢ x;
otherwise, x ⊙... | {
"game_data": {
"answer": "325",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 6 ⊙ 4",
"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 = x + x + y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * 1 + y.
and ○, the rules are as follows:
on the real number field, x ○ y = x * y + y.
The precedence of operations: ** = ⊗ > * = / = % = ○ > + = - = ⊕。
Parentheses... | {
"game_data": {
"answer": "111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 8 ⊗ 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 x is even, x □ y = y * abs(3 - x * x);
otherwise, x □ y = x * y + 3 * x.
and ○, the rules are as follows:
when x is a multiple of 5, x ○ y = (x * y) □ y * 4;
otherwise, x ○ y = x * x + y / y.
The precedence of operations: □ = ○ > ** > * = / = % > + = -。
Parentheses have ... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 8 % 4 □ 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 + y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (1 + y * x) - x.
The precedence of operations: ** > * = / = % = ☆ = ⊗ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is c... | {
"game_data": {
"answer": "31",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 7",
"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 is less than y, x ♡ y = x + y ** y - y;
otherwise, x ♡ y = x * (y).
and □, the rules are as follows:
when x is odd, x □ y = y + y - x;
otherwise, x □ y = x * x + x * y.
and ○, the rules are as follows:
when x is equal to y, x ○ y = x / y + x ♡ y;
otherwise, x ○ y = ... | {
"game_data": {
"answer": "160",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 8 ♡ 8",
"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等于y时，x ◇ y = 2 - 2 + (1 ** x) / y；
其他情况下，x ◇ y = y * y + x + 1。
和 ⊗，规则如下：
当x和y的和是奇数时，x ⊗ y = x + 3 * 1 ◇ y；
其他情况下，x ⊗ y = x ◇ 2 - 4 + y。
和 ⊕，规则如下：
实数域上，x ⊕ y = y ◇ y - y * x - y。
运算优先级：◇ > ** > * = / = % = ⊗ > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ⊗ 3 ◇ 7 ⊕ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-16883.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 3 ◇ 7 ⊕ 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 = y * x。
和 ◇，规则如下：
实数域上，x ◇ y = x ⊕ y。
和 ♢，规则如下：
实数域上，x ♢ y = (y * x ** x)。
运算优先级：♢ > ** > * = / = % = ◇ > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ⊕ 4 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "120",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 4 ◇ 5",
"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x和y都是奇数时，x ⊙ y = abs(y) * y + x；
其他情况下，x ⊙ y = y * y / x - y。
和 ♢，规则如下：
实数域上，x ♢ y = x * y ** 1 * x。
和 ♡，规则如下：
当x是奇数时，x ♡ y = 4 ** 3 ⊙ y + x；
其他情况下，x ♡ y = 5 + y + x。
运算优先级：⊙ > ♢ = ♡ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊙ 2 ♡ 7 ♢ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "864",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 2 ♡ 7 ♢ 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 = x * abs(y)。
和 ◇，规则如下：
当x等于y时，x ◇ y = x * x ◎ y * y * y；
其他情况下，x ◇ y = x + y + x * y ◎ y。
运算优先级：◇ > ** > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ◇ 3 - 5 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 3 - 5 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 ⊗，规则如下：
当y是3的倍数时，x ⊗ y = 4 ** y ** x * y + y；
其他情况下，x ⊗ y = y + x * y * x - x。
和 △，规则如下：
实数域上，x △ y = abs(5 / x ** 3) - y。
和 □，规则如下：
当x等于y时，x □ y = (1 - 3 * y) - x；
其他情况下，x □ y = x * x / y。
运算优先级：⊗ = △ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 □ 8 △ 9 ⊗ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.469188",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 8 △ 9 ⊗ 2",
"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 = abs(y + x + y - x - x).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y - 3 * 2 ◎ (x) * y.
The precedence of operations: ◎ > ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the par... | {
"game_data": {
"answer": "-423",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 9",
"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 + y - x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 △ 8
Please fill your final an... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 8",
"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 = x - x + y * y + x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = (x - 4 ♢ 2) + y * y.
and ◎, the rules are as follows:
when x is equal to y, x ◎ y = 2 * y * x + x - y;
otherwise, x ◎ y = x + y - x - 5.
The precedence of o... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 8 ♢ 4 ◎ 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 the sum of x and y is even, x ○ y = y + x;
otherwise, x ○ y = abs(y * y + x).
and ☆, the rules are as follows:
when the sum of x and y is even, x ☆ y = 4 * x / y / 2;
otherwise, x ☆ y = (y * 3) + x.
The precedence of operations: ○ > ** > * = / = % > + = - = ☆。
Parenthese... | {
"game_data": {
"answer": "37",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 9",
"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 - abs(y).
and ◇, the rules are as follows:
on the real number field, x ◇ y = y + x - 1.
The precedence of operations: ◎ > ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calcul... | {
"game_data": {
"answer": "66",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 6 ◎ 4 * 7 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 △，规则如下：
当x小于y时，x △ y = x + y / y - 5；
其他情况下，x △ y = abs(5 * y * x + x)。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 △ 10 % 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 10 % 5",
"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。
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": "8",
"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 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y / x * y - 3。
和 △，规则如下：
实数域上，x △ y = y * x + 5 ⊗ x。
和 ♡，规则如下：
实数域上，x ♡ y = (x - x + x) * y / y。
运算优先级：△ > ** > * = / = % = ⊗ = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊗ 3 ♡ 5 ⊗ 4 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-607.823333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 3 ♡ 5 ⊗ 4 △ 8",
"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 = y + y * 3 - x - y。
和 ⊗，规则如下：
当x是奇数时，x ⊗ y = y * y - x - 3 * x；
其他情况下，x ⊗ y = y - x - x。
运算优先级：** > * = / = % = ♡ = ⊗ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊗ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "72",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 10",
"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 + x * 4.
The precedence of operations: ** > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ◇ 6 + 4 ◇ 2
Please fi... | {
"game_data": {
"answer": "38",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 6 + 4 ◇ 2",
"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 greater than y, x □ y = y + 4 / x;
otherwise, x □ y = y - x ** x.
and ⊙, the rules are as follows:
when y is a multiple of 5, x ⊙ y = x / y;
otherwise, x ⊙ y = (y / x) / x.
The precedence of operations: ⊙ > ** > * = / = % = □ > + = -。
Parentheses have the highest pr... | {
"game_data": {
"answer": "6.292893",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 10 □ 7",
"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 = x + 5 * y.
and □, the rules are as follows:
on the real number field, x □ y = y + x * abs(y).
and ◎, the rules are as follows:
when x is less than y, x ◎ y = (4 ** x □ y);
otherwise, x ◎ y = (x + y) / 4.
The precedence of operations: ◎ > ** >... | {
"game_data": {
"answer": "48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 5 ⊗ 9",
"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和y的和是偶数时，x ⊕ y = y + x + x；
其他情况下，x ⊕ y = x / y。
和 ○，规则如下：
实数域上，x ○ y = y ⊕ (x ** y)。
和 ♡，规则如下：
当x大于y时，x ♡ y = y + x；
其他情况下，x ♡ y = x + 5 + y。
运算优先级：⊕ = ○ > ** = ♡ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 4 ○ 4 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "58.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 4 ○ 4 ⊕ 5",
"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 + y - x.
and ◎, the rules are as follows:
when x is a multiple of 3, x ◎ y = x * y - x;
otherwise, x ◎ y = x ◇ y.
The precedence of operations: ◎ > ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside t... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 4 ◇ 1 + 9",
"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 * x ** y.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 / 9 ○ 1 * 3
Please fill your... | {
"game_data": {
"answer": "0.624295",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 / 9 ○ 1 * 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 ◇，规则如下：
当y是偶数时，x ◇ y = 1 - y - x + 2 - x；
其他情况下，x ◇ y = y + (x + y - y ** y)。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1
请将最终答案填入\boxed{}中。 | {
"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 | Define ♡, the rules are as follows:
when y is a multiple of 3, x ♡ y = 1 - (x / y / x);
otherwise, x ♡ y = y - y + x.
and □, the rules are as follows:
when y is a multiple of 3, x □ y = (x ** y);
otherwise, x □ y = abs(y * x).
The precedence of operations: □ > ♡ > ** > * = / = % > + = -。
Parentheses have the hi... | {
"game_data": {
"answer": "64",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 6 ♡ 7",
"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 x is odd, x ⊕ y = 3 - x / y;
otherwise, x ⊕ y = x - x + y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - x * x.
and △, the rules are as follows:
when x is odd, x △ y = (x) ⊙ y;
otherwise, x △ y = y - y - x.
The precedence of operations: ⊙ > ** ... | {
"game_data": {
"answer": "-2.875",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 8 △ 5 ⊙ 1",
"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 * y + 1 - y * (x).
and △, the rules are as follows:
on the real number field, x △ y = abs(x) ** y.
and ⊙, the rules are as follows:
when x is a multiple of 5, x ⊙ y = y △ x - x + x;
otherwise, x ⊙ y = x / y ⊕ 3 - x - x.
The precedence of op... | {
"game_data": {
"answer": "-19417.808291",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊙ 7 △ 5 ⊕ 2",
"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的和是奇数时，x ◇ y = 3 / x - y + x；
其他情况下，x ◇ y = x * x / 5 * y * x。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 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x和y都是偶数时，x ♢ y = (x) / y；
其他情况下，x ♢ y = x - x * y。
和 △，规则如下：
实数域上，x △ y = x - x / y。
和 ☆，规则如下：
实数域上，x ☆ y = x + x - y。
运算优先级：△ > ** = ☆ > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ☆ 7 ☆ 7 △ 2 ♢ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-129.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 7 ☆ 7 △ 2 ♢ 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 = x - (y * x - y).
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 △ 8
Please fill your fi... | {
"game_data": {
"answer": "-41",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 8",
"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 = x * x - y.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ▽ 6
Please fill your final an... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 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 = y * y - y ** x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = abs(x) + y.
The precedence of operations: ** > * = / = % = ◎ > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calcu... | {
"game_data": {
"answer": "-78100",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 5",
"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 even, x ♢ y = 1 / x ** y;
otherwise, x ♢ y = x - y + x + 1.
and ⊕, the rules are as follows:
when x is equal to y, x ⊕ y = x - y - y;
otherwise, x ⊕ y = (x) - x + 2 - y.
and ⊙, the rules are as follows:
when x is odd, x ⊙ y = y ** x + y + x;
otherwise, x ⊙ y = y... | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 2 ♢ 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:
when x is less than y, x ⊕ y = x / y;
otherwise, x ⊕ y = 3 / x - y.
and ☆, the rules are as follows:
when x is less than y, x ☆ y = x ⊕ y * y;
otherwise, x ☆ y = y + x.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = y + x * x;
otherwise, x ♡ y = ... | {
"game_data": {
"answer": "-11.795918",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ☆ 6 ⊕ 4 ⊕ 2 ♡ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 △，规则如下：
当x小于y时，x △ y = y * y * x + x - y；
其他情况下，x △ y = y * y - x - x + x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"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等于y时，x △ y = 5 * x * y；
其他情况下，x △ y = 5 - abs(y + x)。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 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:
when x and y are both even, x ○ y = y + y - x + y * x;
otherwise, x ○ y = 3 * y - x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = 1 ○ x - 3 + y.
and ◇, the rules are as follows:
when x is a multiple of 5, x ◇ y = 1 - y / y - x - x;
otherwise, x ◇ y = x... | {
"game_data": {
"answer": "235",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 6 ◇ 1 ♢ 8",
"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 = 2 - x * y。
和 ○，规则如下：
实数域上，x ○ y = 5 + y / 4 - x。
运算优先级：○ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ◎ 10 ○ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◎ 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：
当x和y的和是偶数时，x ⊕ y = x + y + y；
其他情况下，x ⊕ y = x - y + x。
和 □，规则如下：
当x和y的和是奇数时，x □ y = (x + y + y)；
其他情况下，x □ y = y + y ⊕ x。
和 ⊗，规则如下：
实数域上，x ⊗ y = abs(y + x) * x。
运算优先级：□ > ** > * = / = % = ⊕ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ⊕ 1 □ 8 □ 5 ⊗ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-520",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 1 □ 8 □ 5 ⊗ 6",
"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 = y - (y) - x。
和 ⊙，规则如下：
实数域上，x ⊙ y = x + y。
运算优先级：** > * = / = % = ☆ > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ☆ 10 ⊙ 6 ⊙ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 10 ⊙ 6 ⊙ 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 = x + y * x * x。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 * 3 ◇ 3 + 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "994",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 * 3 ◇ 3 + 4",
"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 equal to y, x □ y = (y + x) - 4;
otherwise, x □ y = y - 4 + x + 2 - x.
and ♡, the rules are as follows:
when y is odd, x ♡ y = y - x / (x * x);
otherwise, x ♡ y = y - 5 - abs(1) * x * 4.
The precedence of operations: ♡ > ** > * = / = % = □ > + = -。
Parentheses have ... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 4",
"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) * 3 + x.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = x - x * y;
otherwise, x ♡ y = 4 - x + x * y.
and ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = x + y * x;
otherwise, x ▽ y = x + y.
The ... | {
"game_data": {
"answer": "39",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 8 ▽ 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 x and y are both even, x △ y = 5 + x - y ** y * x;
otherwise, x △ y = y + y - x - y - y.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 4 △ 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 - abs(x + x).
and ☆, the rules are as follows:
when x and y are both odd, x ☆ y = y + y + x;
otherwise, x ☆ y = abs(y - x * y).
and ⊕, the rules are as follows:
when y is odd, x ⊕ y = y * x * y;
otherwise, x ⊕ y = abs(x / y).
The preceden... | {
"game_data": {
"answer": "376.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 10 ⊗ 8 ☆ 9 * 6",
"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 = abs(y + x * y).
and ♡, the rules are as follows:
when x is even, x ♡ y = x □ y - x;
otherwise, x ♡ y = x - (y) - x.
The precedence of operations: □ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression inside t... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 2",
"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 = x + x - y / x * x.
and □, the rules are as follows:
when x is equal to y, x □ y = x * (y + 3) ♢ 2;
otherwise, x □ y = x * y ♢ y / x.
and ○, the rules are as follows:
when y is a multiple of 3, x ○ y = y - y + x;
otherwise, x ○ y = y / y / x... | {
"game_data": {
"answer": "23.997814",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♢ 4 □ 5 * 3 ○ 4 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null... |
logic-v2 | 定义 ◇，规则如下：
当y是偶数时，x ◇ y = x * y * 4；
其他情况下，x ◇ y = x * y。
和 ○，规则如下：
当x和y都是偶数时，x ○ y = x + (y) - x；
其他情况下，x ○ y = x / y - x。
和 △，规则如下：
当y是3的倍数时，x △ y = y ○ x；
其他情况下，x △ y = x + y ◇ x。
运算优先级：◇ = ○ = △ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 6 ◇ 3 ○ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 6 ◇ 3 ○ 4",
"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 = x * y * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * y * x.
and △, the rules are as follows:
when x and y are both even, x △ y = x * y + x;
otherwise, x △ y = x / y.
The precedence of operations: ⊙ = △ > ** = ⊗ > ... | {
"game_data": {
"answer": "200",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊙ 2 △ 4",
"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 y is a multiple of 5, x ○ y = x + x + y;
otherwise, x ○ y = y * abs(x).
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expressio... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": nu... |
logic-v2 | 定义 □，规则如下：
当x是奇数时，x □ y = y - x * x；
其他情况下，x □ y = x - x * y ** x。
和 ◎，规则如下：
实数域上，x ◎ y = x + 3 □ 2 * y。
运算优先级：□ > ** > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◎ 5 □ 6 / 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "14.1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 5 □ 6 / 10",
"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 + x。
和 △，规则如下：
实数域上，x △ y = x + y。
运算优先级：□ > ** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 △ 9 % 3 - 7 □ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 9 % 3 - 7 □ 4",
"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 = x + y + y + x.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ○ 5
Please fill your fina... | {
"game_data": {
"answer": "26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 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：
实数域上，x □ y = y + x / x。
和 ▽，规则如下：
当x和y都是奇数时，x ▽ y = x * (x * y)；
其他情况下，x ▽ y = (y * 5 + y * x / x)。
运算优先级：▽ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ** 3 ▽ 7 □ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ** 3 ▽ 7 □ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◇，规则如下：
当y是3的倍数时，x ◇ y = x + x * x + y - x；
其他情况下，x ◇ y = y * x + 2 + 3。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ◇ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "17",
"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":... |
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