env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ⊗, the rules are as follows:
when x is less than y, x ⊗ y = x + x + x - y ** x;
otherwise, x ⊗ y = 2 + y + x + 4 + 2.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = (y * x + x) * y.
and ◇, the rules are as follows:
when x is even, x ◇ y = x + y + y + x / y;
otherwise, x ◇ y = x - y ... | {
"game_data": {
"answer": "831.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 10 ◇ 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:
on the real number field, x ◎ y = 4 / y + x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y / x.
and ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = x ** y + y;
otherwise, x ⊗ y = x / x * y.
The precedence of operations: ◎ > ♡ = ⊗ > ** > *... | {
"game_data": {
"answer": "0.130435",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 7 ◎ 6 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y - x + 2 * y。
和 ☆，规则如下：
实数域上，x ☆ y = x / abs(y) / x。
运算优先级：☆ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◎ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 8",
"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 * x * y - y。
和 △，规则如下：
当x小于y时，x △ y = x / y + y；
其他情况下，x △ y = y + 5 ○ 1 * x。
和 ☆，规则如下：
实数域上，x ☆ y = x / 4 * 2 ○ x + y。
运算优先级：○ > ** = △ > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ☆ 10 ○ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "297.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 10 ○ 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 = 3 - y * x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = (5) * y / x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x ⊗ y - x.
The precedence of operations: ◇ > ♢ > ** > * = / = % > + = - = ⊗。
Parenthes... | {
"game_data": {
"answer": "-829.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 8 ◇ 9 ⊗ 7 ♢ 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 = x / y.
and ◇, 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.
P... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 1 ◇ 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 + 4 + 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: 5 ⊗ 9 ◎ 9 ◎ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1376",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 9 ◎ 9 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = 5 ** y - 2 * 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 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15620",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define △, the rules are as follows:
when x is a multiple of 3, x △ y = y * y + y + x * y;
otherwise, x △ y = x + y * x * y * x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value o... | {
"game_data": {
"answer": "68",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 4 △ 1",
"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 = x - y + y - 5 * x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = (y ⊕ x * x + y * y).
and △, the rules are as follows:
on the real number field, x △ y = y - x / x + y + x.
The precedence of operations: ** = ⊕ = △ > * = / = ... | {
"game_data": {
"answer": "11264",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♢ 3 △ 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:
on the real number field, x ♡ y = x * y.
and ♢, the rules are as follows:
when the sum of x and y is odd, x ♢ y = y ♡ y + x / 4;
otherwise, x ♢ y = x + y - x * y.
The precedence of operations: ♢ > ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expres... | {
"game_data": {
"answer": "-17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 7 % 8 ♢ 4",
"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 and y are both even, x ○ y = x * y + y;
otherwise, x ○ y = y / x + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y ○ x - y.
The precedence of operations: ** > * = / = % = ○ = ◎ > + = -。
Parentheses have the highest priority, and the expression ins... | {
"game_data": {
"answer": "-4.714286",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 7",
"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 / x / x - 3.
and △, the rules are as follows:
on the real number field, x △ y = 3 - y / x * 1.
The precedence of operations: ** > * = / = % = ♡ > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 4 △ 2 ♡ 8 + 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x + x + 3 * y。
和 ◇，规则如下：
当x等于y时，x ◇ y = 4 + x - y + y；
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 □ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 □ 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:
when y is a multiple of 3, x ◎ y = y * y - abs(x);
otherwise, x ◎ y = x - y * x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + y - x.
The precedence of operations: ⊕ > ◎ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "0",
"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 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x + y * x - x + x.
and □, the rules are as follows:
when x is greater than y, x □ y = x / x / y * y ☆ x;
otherwise, x □ y = 4 + x * 5 / y - x.
The precedence of operations: ☆ > ** > * = / = % > + = - = □。
Parentheses have the highest priority, ... | {
"game_data": {
"answer": "11",
"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_de... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y * y * 5 * (5 - x)。
和 ⊙，规则如下：
当x是5的倍数时，x ⊙ y = x * (x / y + y) ☆ x；
其他情况下，x ⊙ y = y + (5 ** x) ☆ 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: 1 ☆ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "500",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 5",
"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:
when the sum of x and y is odd, x ◎ y = y ⊕ x ** y;
otherwise, x ◎ y = y ⊕ x.
and ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = (x - y - y);
otherwise, x ⊙ y = y - x ⊕ y.
... | {
"game_data": {
"answer": "770",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 10 ◎ 6",
"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 less than y, x ◇ y = y - x * y - y;
otherwise, x ◇ y = x - abs(y + y) - y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the e... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x - x * y。
和 ⊗，规则如下：
实数域上，x ⊗ y = y + x + x。
运算优先级：⊗ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 □ 8 * 7 ⊗ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1120",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 8 * 7 ⊗ 6",
"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等于y时，x ◎ y = y - 2 + 5 - y + x；
其他情况下，x ◎ y = x + y - y / x * 4。
和 □，规则如下：
实数域上，x □ y = 5 / x ◎ y + 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: 9 ◎ 3 □ 3 - 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2.601329",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 3 □ 3 - 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 ▽，规则如下：
当x和y都是奇数时，x ▽ y = y * 3 * x；
其他情况下，x ▽ y = (y ** 5 * x) + x。
运算优先级：** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◇, the rules are as follows:
when x is equal to y, x ◇ y = 4 + y / 5 - x;
otherwise, x ◇ y = y + 3 - 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 exp... | {
"game_data": {
"answer": "1.125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 2 / 8 + 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y - x * 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: ○ > ** > * = / = % = ⊗ > + = - = ♢。
Parentheses h... | {
"game_data": {
"answer": "-9.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 5 ⊗ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x - (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 □ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 5",
"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 * 1 - y - y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = 1 - y + x - 4 + x.
and □, the rules are as follows:
when y is even, x □ y = x / y + y;
otherwise, x □ y = x * x + y * abs(x - y).
The precedence of operatio... | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 5 □ 4",
"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 the sum of x and y is odd, x ◇ y = y * y * y - (x);
otherwise, x ◇ y = x * y - x + x.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 3 % 10 / 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 = y - x + x / x * x.
and △, the rules are as follows:
on the real number field, x △ y = y * x + x ♡ y * x.
The precedence of operations: ♡ > ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthese... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 % 2 ♡ 3 ♡ 9 △ 3",
"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 and y are both odd, x ⊙ y = x + (y - x);
otherwise, x ⊙ y = x * (y * y).
and □, the rules are as follows:
on the real number field, x □ y = 4 - x ⊙ y.
and ⊕, the rules are as follows:
when y is a multiple of 5, x ⊕ y = (5 + x) ⊙ y;
otherwise, x ⊕ y = y □ 3 + x.
The p... | {
"game_data": {
"answer": "135",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊙ 5 □ 9 ⊕ 4 ⊙ 2",
"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 = x + y + y。
和 ○，规则如下：
当x大于y时，x ○ y = x * y + x + x；
其他情况下，x ○ y = y + x * y * y。
运算优先级：♡ > ** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ○ 7 + 2 ♡ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "78",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 7 + 2 ♡ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 ♢，规则如下：
当x是奇数时，x ♢ y = x - y * x * x；
其他情况下，x ♢ y = (x + y * y + x)。
和 ⊙，规则如下：
实数域上，x ⊙ y = (y - x * x)。
和 ☆，规则如下：
当y是奇数时，x ☆ y = 1 - x / abs(y)；
其他情况下，x ☆ y = y - x * y - y。
运算优先级：⊙ > ** = ☆ > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ☆ 4 ♢ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 4 ♢ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = (x * y + 1) + 3 - x。
和 □，规则如下：
当x是奇数时，x □ y = x + y ◎ y；
其他情况下，x □ y = x - y ** y - x + x。
运算优先级：□ > ◎ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◎ 8 □ 2 / 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "34",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 8 □ 2 / 1",
"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 greater than y, x □ y = x * y * y - 3;
otherwise, x □ y = x - y - x - y.
and ○, the rules are as follows:
when y is a multiple of 5, x ○ y = y * y - x ** y;
otherwise, x ○ y = y + x + x * y.
The precedence of operations: ○ > ** = □ > * = / = % > + = -。
Parentheses h... | {
"game_data": {
"answer": "101",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 8 □ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ◇，规则如下：
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: 5 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "82.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x * abs(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: 9 ◇ 8 / 2 % 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 8 / 2 % 6",
"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 / y - x.
and ♢, the rules are as follows:
when the sum of x and y is odd, x ♢ y = (y) * x;
otherwise, x ♢ y = x * x ◎ y - x.
The precedence of operations: ◎ > ** = ♢ > * = / = % > + = -。
Parentheses have the highest priority, and the expr... | {
"game_data": {
"answer": "-0.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 7 % 9 ◎ 1 / 5",
"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 + y * y - y * x.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6
Please fill your fina... | {
"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：
实数域上，x ⊗ y = x * y / y。
和 ♢，规则如下：
当x等于y时，x ♢ y = (x) ⊗ y；
其他情况下，x ♢ y = y ⊗ x / y。
和 ◎，规则如下：
实数域上，x ◎ y = y * x ⊗ x。
运算优先级：♢ > ** > * = / = % > + = - = ⊗ = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊗ 5 ♢ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 5 ♢ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = 5 * y + 5 + x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 △ 9 ** 3 / 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "913",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 9 ** 3 / 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = x + y + 2 + x - 2;
otherwise, x ▽ y = 3 + x * y - x.
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value... | {
"game_data": {
"answer": "-11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 - 9 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x - abs(x * y).
and ▽, the rules are as follows:
when x is equal to y, x ▽ y = x + x - y;
otherwise, x ▽ y = y + (x - y).
and △, the rules are as follows:
when x is less than y, x △ y = x / abs(x - y);
otherwise, x △ y = y + (x + 2).
The pr... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 9 △ 5 ◎ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y + x - x。
和 ⊙，规则如下：
实数域上，x ⊙ y = x ⊗ y * y。
和 ◇，规则如下：
当y是偶数时，x ◇ y = y * y ⊗ x；
其他情况下，x ◇ y = x + y。
运算优先级：◇ > ** > * = / = % = ⊗ = ⊙ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◇ 10 ⊗ 2 / 1 ⊙ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "49",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 10 ⊗ 2 / 1 ⊙ 7",
"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 = x * y - x.
and □, the rules are as follows:
on the real number field, x □ y = x ♢ y ** y.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = y + x * y;
otherwise, x ♡ y = x ♢ y * 2.
The precedence of operations: □ > ** =... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 5 ♡ 8 ♡ 7 ♢ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x * y + x。
和 △，规则如下：
实数域上，x △ y = x ⊕ x + y。
和 ♡，规则如下：
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: 5 △ 3 ♡ 7 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "320",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 3 ♡ 7 ⊕ 7",
"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 + 2;
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: 5 ▽... | {
"game_data": {
"answer": "-8.555556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 1 ▽ 9",
"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 - y * x - y.
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 3 △ 7
Please fill your ... | {
"game_data": {
"answer": "59",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 3 △ 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:
on the real number field, x □ y = x - 5 * abs(y).
and ⊕, the rules are as follows:
when x and y are both odd, x ⊕ y = y + x * x;
otherwise, x ⊕ y = y - y + x + x.
The precedence of operations: □ > ** > * = / = % > + = - = ⊕。
Parentheses have the highest priority, and the expres... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 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；
其他情况下，x ◎ y = y + 4 * y * x。
和 △，规则如下：
实数域上，x △ y = abs(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 △ 8 ◎ 6 * 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7200",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 8 ◎ 6 * 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = (y - y - y) * x.
and ♢, the rules are as follows:
when x is a multiple of 5, x ♢ y = x * y + x ⊗ y;
otherwise, x ♢ y = (x) * x * y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y - x * y.
The precedence of operations: ⊕ ... | {
"game_data": {
"answer": "-8820",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 6 ♢ 6 ⊕ 1",
"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 + 2 * y.
and ○, the rules are as follows:
on the real number field, x ○ y = 5 / 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": "0.025381",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 3 ⊗ 1 ⊕ 4",
"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 a multiple of 5, x ⊕ y = x * x / y;
otherwise, x ⊕ y = y ** x - y.
and ♡, the rules are as follows:
when y is odd, x ♡ y = x * 1 + y;
otherwise, x ♡ y = y ⊕ x * y.
and ○, the rules are as follows:
on the real number field, x ○ y = y + x * y.
The precedence of oper... | {
"game_data": {
"answer": "67",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 8 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x + y ** (y)。
和 ♡，规则如下：
实数域上，x ♡ y = y + x。
运算优先级：□ = ♡ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 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 = y * x。
和 ⊗，规则如下：
当x是奇数时，x ⊗ y = x + y；
其他情况下，x ⊗ y = (y - 3 * x)。
运算优先级：□ > ** > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 □ 4 ⊗ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-91",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 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 = y * x - x；
其他情况下，x △ y = x / y * y。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 △ 2 / 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 2 / 3",
"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 = 1 - y - x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 1 - (y + x) + 5.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y ** x + y - y.
The precedence of operations: ⊗ = ◇ = ▽ > ** > * = / = % > + = -。
... | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 3 ▽ 7 ⊗ 7 ◇ 4",
"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 - y.
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 calculated ... | {
"game_data": {
"answer": "984.15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 10 ⊗ 4 ☆ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | 定义 ⊙，规则如下：
当x等于y时，x ⊙ y = 2 + (y / 4) + x；
其他情况下，x ⊙ y = y / y + 4 + x。
和 ☆，规则如下：
当y是3的倍数时，x ☆ y = x ** y；
其他情况下，x ☆ y = x ⊙ y * y + y。
和 ◎，规则如下：
实数域上，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: 8 ◎ 2 ⊙ 3 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 2 ⊙ 3 ☆ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y + x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y / x * y.
and ◇, the rules are as follows:
when y is even, x ◇ y = y - x * (x);
otherwise, x ◇ y = (x) * x - y.
The precedence of operations: ** = ♢ = ♡ > * = / = % = ... | {
"game_data": {
"answer": "5618.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 6 ◇ 5 ♡ 2 ♢ 7 + 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * y - x ** y。
和 ⊙，规则如下：
当x是5的倍数时，x ⊙ y = 3 + x - y + x；
其他情况下，x ⊙ y = y / x - y + 4。
运算优先级：** = ⊙ > * = / = % > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 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": "1 □ 4 ⊙ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x - x * y.
and □, the rules are as follows:
when x is even, x □ y = x ◎ y;
otherwise, x □ y = y - x + x.
The precedence of operations: ◎ > ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthe... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = 3 - y * x.
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 calculated ... | {
"game_data": {
"answer": "-218",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 5 ♡ 3 ⊗ 7",
"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 - x ♢ x ** y。
和 ○，规则如下：
实数域上，x ○ y = x + 3 * x - y。
运算优先级：♢ = ○ > ** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ○ 10 ♢ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 10 ♢ 7",
"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。
和 ⊕，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：
实数域上，x ☆ y = y ⊗ 2 + x。
运算优先级：⊗ > ** > * = / = % = ⊕ > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 * 2 ☆ 2 ⊗ 1 + 10 ⊕ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 * 2 ☆ 2 ⊗ 1 + 10 ⊕ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ▽, the rules are as follows:
when y is a multiple of 5, x ▽ y = y - abs(x / 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 expressio... | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 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.
and ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = y △ x + y;
otherwise, x ⊙ y = x - y * x.
The precedence of operations: △ > ** > * = / = % > + = - = ⊙。
Parentheses have the highest priority, and the expression insi... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 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 * (y - x).
and ◇, the rules are as follows:
when x is less than y, x ◇ y = y * x - y - y;
otherwise, x ◇ y = x ⊙ 3 - y + (x).
and ◎, the rules are as follows:
on the real number field, x ◎ y = y / x ** x + x.
The precedence of operation... | {
"game_data": {
"answer": "-41",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 1 ◎ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ♢, the rules are as follows:
when x is a multiple of 3, x ♢ y = x ** 4 / x ** x + y;
otherwise, x ♢ y = 3 + y - x - 2 - x.
and ◎, the rules are as follows:
when y is even, x ◎ y = y + x ** y;
otherwise, x ◎ y = y * x * x - x + x.
and ☆, the rules are as follows:
when x is a multiple of 3, x ☆ y = y - x... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 4 ☆ 3 ♢ 1 ◎ 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 y is a multiple of 3, x ▽ y = y * y + x / x * y;
otherwise, x ▽ y = 5 - 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 o... | {
"game_data": {
"answer": "15",
"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_depth":... |
logic-v2 | Define △, the rules are as follows:
when y is odd, x △ y = y / (1 * x);
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 expression: 5 △ 8
P... | {
"game_data": {
"answer": "13",
"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 | Define △, the rules are as follows:
when x is greater than y, x △ y = abs(y - x - y) - 2;
otherwise, x △ y = y + x + x / x.
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of th... | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 4 △ 8",
"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 = y - x * x;
otherwise, x ⊗ y = y - x - x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (y) - x - x.
and □, the rules are as follows:
when y is odd, x □ y = y - y / x;
otherwise, x □ y = 3 ☆ y + x.
The precedence of operations: ** ... | {
"game_data": {
"answer": "32.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 2 □ 6 / 6 ☆ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ◇, the rules are as follows:
when x is a multiple of 3, x ◇ y = y + y - 1 + x;
otherwise, x ◇ y = x + 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 e... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 10 ◇ 5 ** 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 = 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: 7 ◇ 1
Please fill your final ... | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◇ 1",
"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 greater than y, x ☆ y = x - x - y;
otherwise, x ☆ y = x - (3 - y).
and ◎, the rules are as follows:
on the real number field, x ◎ y = y ☆ x * y.
The precedence of operations: ** = ◎ > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression ins... | {
"game_data": {
"answer": "-9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 10 ☆ 9",
"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是3的倍数时，x ◎ y = (y * x)；
其他情况下，x ◎ y = y + x ** 4。
和 ⊙，规则如下：
当x是5的倍数时，x ⊙ y = x ◎ y；
其他情况下，x ⊙ y = x * x / y。
运算优先级：** = ⊙ > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 / 6 + 9 ⊙ 9 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10009",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 / 6 + 9 ⊙ 9 ◎ 9",
"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 = x - x / y * 5 * x;
otherwise, x △ y = x - y - y - x * x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the va... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 △，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: 4 / 8 / 7 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.038462",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 / 8 / 7 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y * y + (x) / y.
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 = y ⊕ x - x + x.
The precedence of operations: ** > * = / = % = ♡ > + = - = ♢ = ⊕。
P... | {
"game_data": {
"answer": "-4095.90625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 4 ♡ 8 ** 2 ⊕ 8",
"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 a multiple of 3, x □ y = y * x - x + x;
otherwise, x □ y = y - y - y * x - x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y / x + y + x.
The precedence of operations: □ > ** = ⊗ > * = / = % > + = -。
Parentheses have the highest priority, and the... | {
"game_data": {
"answer": "-8.157895",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 / 6 ⊗ 3 % 1 □ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 □，规则如下：
当x等于y时，x □ y = 5 - x ** y + x * y；
其他情况下，x □ y = abs(x - y + x - y) + x。
和 ☆，规则如下：
当y是5的倍数时，x ☆ y = x / y * (x - x * y)；
其他情况下，x ☆ y = x - y - x + x - y。
运算优先级：□ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ☆ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-14.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = (y + x) * y ** 1.
and ⊗, the rules are as follows:
when x is equal to y, x ⊗ y = y - y * x - y;
otherwise, x ⊗ y = x ** abs(y + x) * x.
The precedence of operations: ⊗ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, and the... | {
"game_data": {
"answer": "4545",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊗ 7 + 7 □ 2 ** 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 = y * x * y - 3 - y.
and △, the rules are as follows:
on the real number field, x △ y = 2 * y ♡ x.
The precedence of operations: ** > * = / = % = ♡ = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "-306",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 8 - 7 ♡ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ○，规则如下：
当x小于y时，x ○ y = y + x * x；
其他情况下，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: 9 ○ 7 ○ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "55",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 7 ○ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ▽，规则如下：
当x和y都是奇数时，x ▽ y = x - y * y / x；
其他情况下，x ▽ y = x + y * y - x / y。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 - 6 ▽ 1 ** 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2.666667",
"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,
... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y + 2 ** x + y - y。
和 ☆，规则如下：
当x等于y时，x ☆ y = 1 * 1 * y * x ▽ 2；
其他情况下，x ☆ y = y + y - 1 ▽ x。
和 ⊕，规则如下：
实数域上，x ⊕ y = y - (x + y + 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: 6 ☆ 3 ⊕ 9 / 5 ▽ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-9.105263",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 3 ⊕ 9 / 5 ▽ 6",
"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 + y - x.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 △ 6
Please fill your ... | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ◇，规则如下：
当y是3的倍数时，x ◇ y = x * y + 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: 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:
on the real number field, x ♡ y = x * y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * y + y.
The precedence of operations: ** > * = / = % = ♡ > + = - = ⊕。
Parentheses have the highest priority, and the expression inside the parentheses is calculated firs... | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 9 % 6 ♡ 6 ⊕ 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 = x * y - y / y - y.
and □, the rules are as follows:
on the real number field, x □ y = y * x * 3 - 1 ** x.
and ☆, the rules are as follows:
when the sum of x and y is odd, x ☆ y = y ** x / x;
otherwise, x ☆ y = x - x * y.
The precedence of ope... | {
"game_data": {
"answer": "-1074",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 □ 4 ♢ 7 ☆ 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 + abs(x + 1) * y.
and ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = 3 - y ◎ x + y;
otherwise, x ▽ y = y + 1 + x + x.
The precedence of operations: ** = ◎ > * = / = % = ▽ > + = -。
Parentheses have the highest priority, ... | {
"game_data": {
"answer": "70",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 5 ◎ 8",
"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 = x + y.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ** 1 △ 9
Please fill your final a... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ** 1 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y + abs(x) * x / x。
和 ⊙，规则如下：
当y是3的倍数时，x ⊙ y = x / y ⊕ x ** y；
其他情况下，x ⊙ y = 4 * x + (y / y)。
和 □，规则如下：
当x是偶数时，x □ y = y + 5 * y ⊙ x；
其他情况下，x □ y = x * y ⊕ y。
运算优先级：⊕ > ** > * = / = % = ⊙ > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 □ 4 ⊙ 5 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "170",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 4 ⊙ 5 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ⊕, the rules are as follows:
when y is a multiple of 5, x ⊕ y = 1 + y * x;
otherwise, 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: ⊕ > ** > * = / ... | {
"game_data": {
"answer": "0.000244",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 7 ◇ 2",
"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 and y are both even, x ⊕ y = x * (y) + x / y;
otherwise, x ⊕ y = y + 2 ** x - y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y * (y) ⊕ x + y.
and ◎, the rules are as follows:
when x is a multiple of 3, x ◎ y = x + x + 5 + y;
otherwise, x ◎ y = ... | {
"game_data": {
"answer": "4096",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 1 ◎ 1 ⊕ 5",
"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 - 1 * 5) + x。
运算优先级：** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ** 5 ○ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 5 ○ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = 5 - y - y + x - 3.
and ○, the rules are as follows:
when x is less than y, x ○ y = y + x;
otherwise, x ○ y = x - y - x - x ◎ x.
The precedence of operations: ○ > ** > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the express... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 10",
"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等于y时，x ○ y = y - x * x - x / y；
其他情况下，x ○ y = y - x * y / x + y。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define □, the rules are as follows:
when x is equal to y, x □ y = abs(y * y) * x / x;
otherwise, x □ y = 5 - y + y - x.
and ◇, the rules are as follows:
when y is odd, x ◇ y = 3 - x □ 3 / y;
otherwise, x ◇ y = y / y * x.
The precedence of operations: □ > ** > * = / = % > + = - = ◇。
Parentheses have the highest ... | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 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 = x - y + x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y * x * y.
The precedence of operations: ☆ > ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "-62",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 1 ☆ 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：
实数域上，x ♢ y = x * y - 2 / x ** y。
运算优先级：** > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 % 3 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 % 3 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
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