env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = 4 * x * x * y + x.
and ◎, the rules are as follows:
when x is a multiple of 5, x ◎ y = y + y - x + y - y;
otherwise, x ◎ y = x / y ⊗ x * y * x.
and △, the rules are as follows:
on the real number field, x △ y = (x * x) + y.
The precedence of ... | {
"game_data": {
"answer": "731.22194",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 4 △ 9 ⊗ 9 ◎ 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。
和 ▽，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 = y + x - x；
其他情况下，x ♡ y = y - y + x。
运算优先级：▽ > ** = ⊙ > * = / = % > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ▽ 10 ⊙ 10 ♡ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 10 ⊙ 10 ♡ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ⊗, the rules are as follows:
when x is even, x ⊗ y = y - y + x;
otherwise, x ⊗ y = y + x * y.
and △, the rules are as follows:
on the real number field, x △ y = y * y - x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = 5 * abs(y * x).
The precedence of operations: ▽ > ** = △ > * = / =... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 10 ▽ 6",
"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 * 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: 1 * 1 ** 8 ▽ 6
Please fill your... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 * 1 ** 8 ▽ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ◇，规则如下：
当x等于y时，x ◇ y = 1 * y * x + x / x；
其他情况下，x ◇ y = 4 * x + x / y。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ◇ 2 ◇ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 2 ◇ 10",
"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 = abs(y - x * 3)。
和 ♡，规则如下：
当x小于y时，x ♡ y = x ☆ y + x - x；
其他情况下，x ♡ y = x - y * x + y。
运算优先级：** > * = / = % = ☆ > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ☆ 4 - 6 ♡ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 4 - 6 ♡ 7",
"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。
和 ◇，规则如下：
当y是5的倍数时，x ◇ y = x + (x - y)；
其他情况下，x ◇ y = x ♢ y + 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: 7 ♢ 4 ◇ 8 □ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "53829",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 4 ◇ 8 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y + x + x。
和 △，规则如下：
当x是偶数时，x △ y = (x) ** y；
其他情况下，x △ y = abs(x - y - y)。
和 ♢，规则如下：
实数域上，x ♢ y = x + 3 / y。
运算优先级：△ > ** = □ > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 △ 1 □ 9 ♢ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 1 □ 9 ♢ 3",
"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。
和 ▽，规则如下：
实数域上，x ▽ y = 1 + 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 ▽ 1 ▽ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "28",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 2 ▽ 1 ▽ 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x和y都是奇数时，x ◎ y = x + abs(2 - y)；
其他情况下，x ◎ y = y - y - x。
和 ♡，规则如下：
当y是5的倍数时，x ♡ y = 2 ** 5 ** y - x；
其他情况下，x ♡ y = y + x + x。
和 □，规则如下：
实数域上，x □ y = y / 5 ♡ x + 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 □ 8 ◎ 5 ♡ 6 / 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4.671875",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 8 ◎ 5 ♡ 6 / 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是奇数时，x ♢ y = y + x + y；
其他情况下，x ♢ y = x + y + y。
和 ▽，规则如下：
实数域上，x ▽ y = y + x ♢ 2。
和 ⊕，规则如下：
实数域上，x ⊕ 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: 7 ⊕ 8 ⊕ 9 ♢ 2 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "384",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 8 ⊕ 9 ♢ 2 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define ⊙, the rules are as follows:
when x is even, x ⊙ y = x - y - 1 * x;
otherwise, x ⊙ y = x + x - x / y.
and ◎, the rules are as follows:
when x is greater than y, x ◎ y = x + y + x - y;
otherwise, x ◎ y = x * x + y + y.
and △, the rules are as follows:
when x and y are both odd, x △ y = x + y;
otherwise,... | {
"game_data": {
"answer": "-9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 2 ◎ 2 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ▽, the rules are as follows:
when x and y are both odd, x ▽ y = abs(5 - x) * y / y;
otherwise, x ▽ y = 3 - 1 / x * y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of t... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 2 ** 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ▽，规则如下：
当x和y的和是奇数时，x ▽ y = 1 / y - x；
其他情况下，x ▽ y = x * y - x + y。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ▽, the rules are as follows:
when x is equal to y, x ▽ y = x * x + x ** y;
otherwise, x ▽ y = y - x * x + y.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expres... | {
"game_data": {
"answer": "-58",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x / 4 * y。
和 ♡，规则如下：
当x和y的和是偶数时，x ♡ y = y * y ⊗ x；
其他情况下，x ♡ y = x - y * x。
和 ○，规则如下：
实数域上，x ○ y = x * 5 - y。
运算优先级：○ > ♡ > ** > * = / = % = ⊗ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ⊗ 2 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 2 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define △, the rules are as follows:
when x is greater than y, x △ y = y / x / x;
otherwise, x △ y = x - x + y.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression:... | {
"game_data": {
"answer": "0.078125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 8 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ♡, the rules are as follows:
when x is less than y, x ♡ y = x + y - y;
otherwise, x ♡ y = x + 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 p... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 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 x and y are both odd, x ⊗ y = y / x / 5;
otherwise, x ⊗ y = x * y + 4.
and ◇, the rules are as follows:
on the real number field, x ◇ y = abs(y - x) - x.
and ☆, the rules are as follows:
when y is odd, x ☆ y = y / y - x;
otherwise, x ☆ y = y ⊗ x.
The precedence of oper... | {
"game_data": {
"answer": "-16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 1 ☆ 2 ⊗ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + y + y + y.
and ⊗, the rules are as follows:
when y is a multiple of 3, x ⊗ y = y - x + x * x;
otherwise, x ⊗ y = y ⊙ 3 * x.
and ◎, the rules are as follows:
when x is a multiple of 5, x ◎ y = y ⊙ x * x / y;
otherwise, x ◎ y = 1 ⊙ x - y ... | {
"game_data": {
"answer": "210",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 8 ⊙ 6",
"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 = (1 / y - x).
and ▽, the rules are as follows:
when x is less than y, x ▽ y = x / y;
otherwise, x ▽ y = (x + y - x).
and □, the rules are as follows:
on the real number field, x □ y = y - x - x.
The precedence of operations: ⊗ > ▽ > ** > * = /... | {
"game_data": {
"answer": "6.238095",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 7 / 1 □ 7 ⊗ 3 ⊗ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ◎, the rules are as follows:
when x is odd, x ◎ y = y - x * y ** x * x;
otherwise, x ◎ y = y * x * y * (4).
and ☆, the rules are as follows:
when y is even, x ☆ y = y * 2 * x + x;
otherwise, x ☆ y = x * y * y ◎ x.
The precedence of operations: ◎ > ** > * = / = % = ☆ > + = -。
Parentheses have the highest ... | {
"game_data": {
"answer": "-6864",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 2 % 6 ☆ 3",
"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 = abs(x + y - x)。
和 ◇，规则如下：
实数域上，x ◇ y = y ◎ x + x。
运算优先级：** = ◇ > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ◇ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◇ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x / y * 1.
and ◇, the rules are as follows:
when y is a multiple of 3, x ◇ y = y ⊕ x;
otherwise, x ◇ y = x + x * y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x * y * y.
The precedence of operations: ** > * = / = % = ⊕... | {
"game_data": {
"answer": "960",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 4 ◇ 5",
"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 less than y, x ♢ y = y + y * x - x;
otherwise, x ♢ y = x + y - x + x.
and ◇, the rules are as follows:
when the sum of x and y is odd, x ◇ y = y ** (x) * y * y;
otherwise, x ◇ y = x - (y + x).
and ⊕, the rules are as follows:
when x is equal to y, x ⊕ y = x + y ♢ ... | {
"game_data": {
"answer": "-17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◇ 3 ⊕ 7",
"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是5的倍数时，x △ y = abs(x) * 4 - x / y + y；
其他情况下，x △ y = x * x + x + x + y。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 % 4 △ 5
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 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ▽，规则如下：
当x大于y时，x ▽ y = x - y * y - x；
其他情况下，x ▽ y = x - x * x - y。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ▽ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth... |
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 + y - x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y ⊕ y * x.
The precedence of operations: ◇ > ** > * = / = % > + = - = ⊕ = ○。
Parenthes... | {
"game_data": {
"answer": "460",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 8 ◇ 2 ⊕ 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 = y * (4 / 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 = (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 ○ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y / abs(y * x).
and ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = y * x - abs(x);
otherwise, x ▽ y = x + x - y.
The precedence of operations: ** > * = / = % = □ = ▽ > + = -。
Parentheses have the highest priority, and the... | {
"game_data": {
"answer": "0.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 4 □ 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 even, x ♡ y = x + y - y * x + y;
otherwise, x ♡ y = y + y - x - y - y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y ♡ y + x.
The precedence of operations: ◇ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 7 ◇ 3 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define △, the rules are as follows:
when x is less than y, x △ y = y - x * y + y - x;
otherwise, x △ y = abs(y + x) * x.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the e... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 8 △ 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 even, x ☆ y = y + x * x + y;
otherwise, x ☆ y = x / y + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y - (4 ☆ 3).
The precedence of operations: ** > * = / = % = ⊗ > + = - = ☆。
Parentheses have the highest priority, and the... | {
"game_data": {
"answer": "17.233333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 7 - 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 = x * y。
和 ○，规则如下：
实数域上，x ○ y = x - y * 3。
和 △，规则如下：
实数域上，x △ y = x - y * 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 + 3 ⊕ 2 △ 9 ○ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-140",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 9 + 3 ⊕ 2 △ 9 ○ 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的和是奇数时，x ◇ y = x - y / y + x * 4；
其他情况下，x ◇ y = x + 3 - 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 ◇ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-97",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 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 = abs(x + y).
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 △ 9 / 6
Please fill your fi... | {
"game_data": {
"answer": "3.166667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 9 / 6",
"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 = abs(4) * x * y.
and ♡, the rules are as follows:
when y is even, x ♡ y = x + y - y + x;
otherwise, x ♡ y = y - abs(y + x).
The precedence of operations: ♡ > ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expression i... | {
"game_data": {
"answer": "50",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 - 4 □ 3 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x / y + y.
and △, the rules are as follows:
when y is odd, x △ y = x ** y ** 5;
otherwise, x △ y = x - x - y.
The precedence of operations: □ > △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the par... | {
"game_data": {
"answer": "-10.3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 3 □ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ▽，规则如下：
当y是5的倍数时，x ▽ y = y * abs(5 - y * x)；
其他情况下，x ▽ y = y + y * y + x + x。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ▽ 4 * 2 ** 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4352",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 4 * 2 ** 7",
"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和y都是奇数时，x ◎ y = x + 5 * 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 = 4 - 3 * y ◎ x；
其他情况下，x ⊕ y = x ◎ y / (3 - 5) - y。
和 ⊙，规则如下：
实数域上，x ⊙ y = abs(5 - 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 ⊙ 4 ⊕ 2 + 2 ◎ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊙ 4 ⊕ 2 + 2 ◎ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ◇, the rules are as follows:
when y is even, x ◇ y = x + y - (x - x);
otherwise, x ◇ y = x - y * 3 + 4.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression:... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 % 8 % 7 ◇ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = (x - x) + 3 - y。
和 △，规则如下：
实数域上，x △ y = x - 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: 4 △ 6 □ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 6 □ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊗, the rules are as follows:
when x is less than y, x ⊗ y = 4 * y * y * x;
otherwise, x ⊗ y = x * x * x - y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y ⊗ y - x.
and ◎, the rules are as follows:
when y is even, x ◎ y = x - x ◇ y * x;
otherwise, x ◎ y = y + x + y * x.
The preced... | {
"game_data": {
"answer": "-1979",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 1 ⊗ 8 ◇ 6",
"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的和是奇数时，x ⊗ y = y * x；
其他情况下，x ⊗ y = x ** 4 + y。
和 ♡，规则如下：
实数域上，x ♡ y = x * (y + y)。
和 ⊙，规则如下：
实数域上，x ⊙ y = 1 + y + x。
运算优先级：⊙ > ⊗ > ** = ♡ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 / 8 ⊙ 10 ⊗ 3 ♡ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3e-06",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 / 8 ⊙ 10 ⊗ 3 ♡ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define △, the rules are as follows:
when x is a multiple of 5, x △ y = abs(x + x * x + y) + x;
otherwise, x △ y = 2 + 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 va... | {
"game_data": {
"answer": "-53.222222",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 / 9 △ 8",
"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 / abs(y * x)。
和 ▽，规则如下：
实数域上，x ▽ y = x * y * 5。
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: 1 ▽ 3 ⊙ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "675",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 3 ⊙ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = abs(y - 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: 3 ○ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"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:
on the real number field, x ⊕ y = y * x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = abs(x * y + y).
and ○, the rules are as follows:
on the real number field, x ○ y = y / x - y.
The precedence of operations: ⊗ > ** = ○ > * = / = % = ⊕ > + = -。
Parenthese... | {
"game_data": {
"answer": "-0.214286",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 2 ○ 9 / 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是偶数时，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
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 | 定义 ♢，规则如下：
当y是奇数时，x ♢ y = x - y * y * y；
其他情况下，x ♢ y = y + x + 2。
和 ♡，规则如下：
实数域上，x ♡ y = abs(x) + y - x * x。
和 ⊙，规则如下：
当y是偶数时，x ⊙ y = x ♡ y - x * y；
其他情况下，x ⊙ y = y * x - 5 / 5。
运算优先级：♢ > ** = ⊙ > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ⊙ 3 ♢ 3 ♡ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1715",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊙ 3 ♢ 3 ♡ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define △, the rules are as follows:
when x and y are both even, x △ y = abs(x - y - y / y * x);
otherwise, x △ y = y * (x - x * y - x).
and ▽, the rules are as follows:
when x and y are both odd, x ▽ y = y * x * y * y △ x;
otherwise, x ▽ y = y / y + x ** x + x.
and □, the rules are as follows:
on the real numbe... | {
"game_data": {
"answer": "540",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 6 □ 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y是3的倍数时，x □ y = 4 * x + y + x / 5；
其他情况下，x □ y = 5 * x + y - y - 3。
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: 9 □ 9 ▽ 9 ** 2 / 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "42",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 9 ▽ 9 ** 2 / 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define △, the rules are as follows:
when the sum of x and y is even, x △ y = y - x * y;
otherwise, x △ y = y * y - x.
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expr... | {
"game_data": {
"answer": "-10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 - 6 △ 5",
"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) * x。
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 = 4 + (x) ◎ y。
运算优先级：◎ = ⊙ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ◎ 7 % 10 ⊙ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "49",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 7 % 10 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y ** abs(x / x)。
和 ⊕，规则如下：
实数域上，x ⊕ y = x - x * x / y。
和 ⊙，规则如下：
当x大于y时，x ⊙ y = y - x * y + 5；
其他情况下，x ⊙ y = x - y - y + 1。
运算优先级：⊙ > △ = ⊕ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ⊙ 10 △ 6 ⊕ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 10 △ 6 ⊕ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define △, the rules are as follows:
when x is odd, x △ y = y ** x;
otherwise, x △ y = y * abs(x * y * x).
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 △ ... | {
"game_data": {
"answer": "343",
"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 | Define ▽, the rules are as follows:
when x is greater than y, x ▽ y = y + x / (y);
otherwise, x ▽ y = abs(y + x).
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expressi... | {
"game_data": {
"answer": "12",
"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 y is odd, x △ y = y + x - x;
otherwise, x △ y = 4 / 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: 4 △ 1
Plea... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 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：
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 ○ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ♡, the rules are as follows:
when x is odd, x ♡ y = 3 / x * y;
otherwise, x ♡ y = x * (y) - 4 / x.
and ♢, 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... | {
"game_data": {
"answer": "-32",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 9 ♡ 5",
"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 = abs(x - y) + y * y - x。
和 ♡，规则如下：
当x和y都是偶数时，x ♡ y = y - y ⊕ y / y / (x)；
其他情况下，x ♡ y = x - y - 4 / x / y。
和 ⊙，规则如下：
当x大于y时，x ⊙ y = y + x + x + x ♡ y；
其他情况下，x ⊙ y = x ** y ⊕ x * x * x。
运算优先级：** > * = / = % = ⊕ = ♡ = ⊙ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ⊙ 7 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "18.917946",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 7 ♡ 8",
"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 + 4 * y + 1.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ▽ 5
Please fill your fin... | {
"game_data": {
"answer": "31",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 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:
on the real number field, x ◎ y = x - y - (y) / 3.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x ** y ◎ x.
The precedence of operations: ◎ > ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calc... | {
"game_data": {
"answer": "-6.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 10",
"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 * 4 * x.
and ⊕, the rules are as follows:
when y is a multiple of 5, x ⊕ y = x - y - y - x;
otherwise, x ⊕ y = x / abs(y ** 2) + y.
and ⊙, the rules are as follows:
when y is odd, x ⊙ y = (1 - x) - 3 - y;
otherwise, x ⊙ y = x + x + x ... | {
"game_data": {
"answer": "-248.999968",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 8 ♢ 7",
"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 + x).
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ▽ 5 % 2 ** 8
Please fill yo... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 5 % 2 ** 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define △, the rules are as follows:
when x is a multiple of 3, x △ y = x / x / y - y;
otherwise, x △ y = x + abs(y - x).
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the e... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 1 △ 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 * y + y.
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 △ 5 * 2 - 3
Please fill y... | {
"game_data": {
"answer": "207",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 5 * 2 - 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = x * y + x - y.
and ◇, the rules are as follows:
when x is even, x ◇ y = x - abs(y) - 3 * y;
otherwise, x ◇ y = x ♡ x * y + 4.
The precedence of operations: ◇ > ** > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the expressio... | {
"game_data": {
"answer": "-247",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 4 ◇ 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：
实数域上，x ⊗ y = y / x * x + x - x。
和 ♡，规则如下：
当x小于y时，x ♡ y = 4 + y / x - x + 5；
其他情况下，x ♡ y = y * y / x - x ⊗ y。
和 ♢，规则如下：
当x和y都是偶数时，x ♢ y = 1 * x + y；
其他情况下，x ♢ y = (x ** y)。
运算优先级：⊗ = ♢ > ** = ♡ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♢ 9 ♡ 7 ♢ 3 ⊗ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 9 ♡ 7 ♢ 3 ⊗ 1",
"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 = y * x。
和 ▽，规则如下：
实数域上，x ▽ y = x ⊙ y * x。
运算优先级：** = ▽ > * = / = % = △ > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 1 ** 9 ▽ 10 ⊙ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-42",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 1 ** 9 ▽ 10 ⊙ 6",
"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 3, x △ y = x + x + x / y;
otherwise, x △ y = 5 - 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 ex... | {
"game_data": {
"answer": "14.777778",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ▽，规则如下：
当x和y都是偶数时，x ▽ y = y - x * 3；
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: 4 ▽ 6 ▽ 8 - 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 6 ▽ 8 - 7",
"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 = 5 - (x + y)。
和 △，规则如下：
当x是5的倍数时，x △ y = y ⊗ x * 1；
其他情况下，x △ y = x / 1 ⊗ x + x * y。
和 ○，规则如下：
实数域上，x ○ y = y - 2 ⊗ x + 3。
运算优先级：⊗ > ** = ○ > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ○ 8 ⊗ 5 △ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 8 ⊗ 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5的倍数时，x ◎ y = y + y - 1 - x；
其他情况下，x ◎ y = y + x + (y - 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: 6 □ 6 ◎ 2 / 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.222222",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 6 ◎ 2 / 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = x + 3 - y - 5 - x；
其他情况下，x ⊕ y = x - 2 + y + 1 - 2。
和 ▽，规则如下：
当x和y的和是偶数时，x ▽ y = y - x * y + 4 - y；
其他情况下，x ▽ y = x * y ⊕ x。
和 ◇，规则如下：
实数域上，x ◇ y = y ▽ (x) + 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: 6 ◇ 6 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "140",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 6 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x ** (1) + y.
and ○, the rules are as follows:
on the real number field, x ○ y = x + x ⊗ y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x * y + abs(x).
The precedence of operations: ◎ > ○ > ** > * = / = % = ⊗ > + = -。
Par... | {
"game_data": {
"answer": "718",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 4 * 2 ○ 10 + 10 ⊗ 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 5, x □ y = y * x * y + y ** y;
otherwise, x □ y = 4 - 5 - y - x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x * y + 3 - x □ y.
The precedence of operations: □ > ** > * = / = % > + = - = ⊙。
Parentheses have the highest priority, an... | {
"game_data": {
"answer": "83",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 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.
and ◎, the rules are as follows:
when x is odd, x ◎ y = x ♡ y * y + x;
otherwise, x ◎ y = y + x - x * x.
The precedence of operations: ** > * = / = % > + = - = ♡ = ◎。
Parentheses have the highest priority, and the expression inside the p... | {
"game_data": {
"answer": "-131",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 6 ◎ 1",
"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 odd, x ♡ y = x * y * y ** 2;
otherwise, x ♡ y = abs(y + y) + y + x.
and △, the rules are as follows:
on the real number field, x △ y = x + y + y + y.
The precedence of operations: △ > ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expressio... | {
"game_data": {
"answer": "25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 8 ♡ 1 - 3 * 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 - x.
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 / 5 / 9 △ 6
Please fill your ... | {
"game_data": {
"answer": "0.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 / 5 / 9 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x * y * x.
and ⊙, the rules are as follows:
when x is equal to y, x ⊙ y = y - y - x;
otherwise, x ⊙ y = 5 / x - y.
The precedence of operations: ♢ = ⊙ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside th... | {
"game_data": {
"answer": "145.555556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 5 % 5 ♢ 6",
"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 = 3 * y * x；
其他情况下，x ○ y = y * y - x。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 - 1 ○ 1 ** 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 - 1 ○ 1 ** 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y / (3 * x - x * 4)。
和 ◇，规则如下：
实数域上，x ◇ y = y ☆ 2 / x + x / 3。
运算优先级：◇ > ** = ☆ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1.166667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 7",
"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 even, x △ y = x + y + y * x;
otherwise, x △ y = (y + 3 + x).
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 △... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 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 + 2 + x.
and □, the rules are as follows:
on the real number field, x □ y = (y) * x ☆ 2.
The precedence of operations: ☆ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calcu... | {
"game_data": {
"answer": "4352",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 7 □ 4 ☆ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ☆, the rules are as follows:
when y is odd, x ☆ y = y - x + x / y + y;
otherwise, x ☆ y = x - x ** (y + x).
and ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = x ☆ y + (x * y) + y;
otherwise, x ⊙ y = (y * 2 * 3 ☆ x) - 4.
The precedence of operations: ☆ > ** = ⊙ > * = / = % > + = -。
P... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 1 ⊙ 6 % 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ▽, the rules are as follows:
when x and y are both even, x ▽ y = x * y + x;
otherwise, x ▽ y = x + y * y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expressio... | {
"game_data": {
"answer": "49",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 3 ▽ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊗，规则如下：
当x是5的倍数时，x ⊗ y = x * y；
其他情况下，x ⊗ y = y ** x * x。
和 ⊕，规则如下：
当x是5的倍数时，x ⊕ y = y - x + y；
其他情况下，x ⊕ y = y - y - x。
和 ▽，规则如下：
当x大于y时，x ▽ y = x / y + x；
其他情况下，x ▽ y = 1 + x ** y。
运算优先级：** = ⊗ > * = / = % = ⊕ > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ⊕ 6 ▽ 1 ⊗ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-728",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 6 ▽ 1 ⊗ 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 = (x + y - x + x - 1).
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 * y - x.
The precedence of operations: ⊕ > ** = ☆ > * = / = % > + = ... | {
"game_data": {
"answer": "10.140845",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 6 ☆ 6 ▽ 10",
"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 = 4 + 4 + y + x.
and ⊕, the rules are as follows:
when x is even, x ⊕ y = y / y * x ☆ x;
otherwise, x ⊕ y = 2 * x * x * y.
The precedence of operations: ** > * = / = % = ☆ = ⊕ > + = -。
Parentheses have the highest priority, and the expression ins... | {
"game_data": {
"answer": "18496",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊕ 1 ☆ 2 ⊕ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define □, the rules are as follows:
when x is a multiple of 3, x □ y = y + 2 - y - x;
otherwise, x □ y = x * (x) / 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 expre... | {
"game_data": {
"answer": "3.34888",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 - 2 * 3 ♡ 4 □ 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 - y + x - y - x.
and ○, the rules are as follows:
on the real number field, x ○ y = y * y - y - x □ x.
The precedence of operations: ** = ○ > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parenthese... | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ◇, the rules are as follows:
when y is even, x ◇ y = x - (y - x);
otherwise, x ◇ y = x ** y.
The precedence of operations: ** > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ◇ 8 / 3
... | {
"game_data": {
"answer": "0.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 8 / 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ♡, the rules are as follows:
when x is less than y, x ♡ y = 2 - x / y;
otherwise, x ♡ y = x - y * x.
and △, the rules are as follows:
on the real number field, x △ y = 5 + x / y.
The precedence of operations: ** > * = / = % = ♡ = △ > + = -。
Parentheses have the highest priority, and the expression inside t... | {
"game_data": {
"answer": "-12.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 8 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ○，规则如下：
当x和y的和是偶数时，x ○ y = x / y；
其他情况下，x ○ y = x + x - y。
运算优先级：** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ○ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define △, the rules are as follows:
when x is odd, x △ y = x - y + x * x;
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 the expression: ... | {
"game_data": {
"answer": "-0.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 5 / 3 △ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ⊗, the rules are as follows:
when the sum of x and y is odd, x ⊗ y = y - x / x;
otherwise, x ⊗ y = x - y + y.
and ○, the rules are as follows:
when x is a multiple of 3, x ○ y = x + y;
otherwise, x ○ y = 4 - y * x.
and △, the rules are as follows:
on the real number field, x △ y = x * y ○ y.
The preced... | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 3 ○ 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 and y are both odd, x ◇ y = (y * 4) - 1 - x * 5;
otherwise, x ◇ y = x * x - x - 5 * y.
The precedence of operations: ** > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value... | {
"game_data": {
"answer": "982",
"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_de... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x + x - y - x - y。
运算优先级：** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ◇ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 3",
"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 / x * x / y；
其他情况下，x ▽ y = x - 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: 10 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.15625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
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