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 = 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: 3 / 7 ○ 7 ○ 6
Please fill your ... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 7 ○ 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 - y。
和 ⊗，规则如下：
当x是3的倍数时，x ⊗ y = x ** y ⊙ y；
其他情况下，x ⊗ y = (y * y - x)。
和 ☆，规则如下：
实数域上，x ☆ y = 1 + y * abs(x)。
运算优先级：⊙ = ⊗ > ** = ☆ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊗ 7 ⊙ 1 ☆ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6910",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊗ 7 ⊙ 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:
when the sum of x and y is even, x ⊗ y = 4 - x * y;
otherwise, x ⊗ y = x - y - abs(y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y - x * x - x.
and ◇, the rules are as follows:
when x and y are both even, x ◇ y = 3 * x ▽ x + y;
otherwise, x ◇ y = x ... | {
"game_data": {
"answer": "31",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 6 ◇ 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 * 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 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 5",
"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大于y时，x ⊕ y = y + y - x * x；
其他情况下，x ⊕ y = x - 5 * y。
和 ⊗，规则如下：
实数域上，x ⊗ y = 5 / y - x ⊕ x。
和 ◇，规则如下：
实数域上，x ◇ y = (y * x + y - y)。
运算优先级：⊕ > ** > * = / = % = ◇ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ⊗ 3 ⊕ 4 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "39.96732",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊗ 3 ⊕ 4 ◇ 9",
"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 = 5 + 4 - y * x。
和 ⊕，规则如下：
实数域上，x ⊕ y = x ⊙ 1 * y。
和 ♡，规则如下：
当x和y都是偶数时，x ♡ y = x - abs(y) * y - y；
其他情况下，x ♡ y = x + y + 4 ⊙ y。
运算优先级：⊙ > ⊕ > ** > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊙ 3 * 3 ♡ 5 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-402",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 3 * 3 ♡ 5 ⊕ 5",
"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 * 2 - y + x - y.
and ☆, the rules are as follows:
when y is a multiple of 3, x ☆ y = x + x * y;
otherwise, x ☆ y = 4 - y ⊕ 1 * 2 - x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y + 4 - x * x ⊕ 1.
The precedence of op... | {
"game_data": {
"answer": "-12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 4 ⊙ 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:
on the real number field, x ☆ y = 3 ** y ** x.
and △, the rules are as follows:
when x is a multiple of 5, x △ y = y + y + 1 ☆ x;
otherwise, x △ y = 2 / x ☆ 5 / y.
The precedence of operations: ** = △ > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expre... | {
"game_data": {
"answer": "184.126533",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 1 ☆ 8 / 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y + x + x.
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 ** 5 + 5 ▽ 6
Please fill your... | {
"game_data": {
"answer": "16823",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ** 5 + 5 ▽ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 ⊗，规则如下：
当x和y的和是奇数时，x ⊗ y = x / y / x * x；
其他情况下，x ⊗ y = y + x - x * y。
和 ⊕，规则如下：
实数域上，x ⊕ y = y * x ⊗ x * x。
和 ◇，规则如下：
实数域上，x ◇ y = 5 - 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 ⊕ 7 ⊗ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "945",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊕ 7 ⊗ 9",
"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 = (y * x * x) + y。
和 ♢，规则如下：
实数域上，x ♢ y = abs(x) * y。
运算优先级：☆ = ♢ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♢ 4 ♢ 2 ☆ 3 - 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3067",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 4 ♢ 2 ☆ 3 - 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ⊕，规则如下：
当x和y都是偶数时，x ⊕ y = x * y；
其他情况下，x ⊕ y = x - x + y。
和 ♡，规则如下：
实数域上，x ♡ y = y * x + x。
和 △，规则如下：
当y是5的倍数时，x △ y = (x + y ♡ y)；
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: 4 ♡ 10 ⊕ 6 △ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.306818",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 10 ⊕ 6 △ 9",
"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 = 5 - 3 - x - (y)。
和 ○，规则如下：
当x是5的倍数时，x ○ y = y * y - x - y - (y)；
其他情况下，x ○ y = x / y + x * 3。
和 ☆，规则如下：
当y是5的倍数时，x ☆ y = y + x + x * y + x；
其他情况下，x ☆ y = y ○ 2 - 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 ☆ 2 ⊗ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 2 ⊗ 4",
"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.
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 ○ 3 / 2 ○ 4
Please fill your ... | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 3 / 2 ○ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y * y - y + x / y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x ◎ y * x.
The precedence of operations: ◎ = ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "84.571429",
"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:
when the sum of x and y is even, x ○ y = x / y + y + y * y;
otherwise, x ○ y = 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 v... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ♢, the rules are as follows:
when x and y are both odd, x ♢ y = y + y - x;
otherwise, x ♢ y = y ** x - y.
and □, the rules are as follows:
when x is greater than y, x □ y = y + x - x;
otherwise, x □ y = y * x + x.
and ☆, the rules are as follows:
when x and y are both even, x ☆ y = (5 + x ** y);
otherw... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 6 ☆ 9 □ 5 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 ⊗，规则如下：
当y是5的倍数时，x ⊗ y = y - x * abs(y + 4)；
其他情况下，x ⊗ y = x + y / x * 2 * x。
和 ◎，规则如下：
实数域上，x ◎ y = x * y * x + x + x。
和 ♢，规则如下：
当x等于y时，x ♢ y = y ◎ y - x / x * y；
其他情况下，x ♢ y = x ⊗ x + y * x。
运算优先级：♢ > ** = ◎ > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊗ 3 ◎ 9 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1315",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 3 ◎ 9 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = x * y。
和 □，规则如下：
实数域上，x □ y = y ▽ x + (y)。
和 ♡，规则如下：
当x等于y时，x ♡ y = (y □ 5) * x；
其他情况下，x ♡ y = 5 + x □ y。
运算优先级：** = ▽ = ♡ > * = / = % = □ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 6 ▽ 6 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "602",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 6 ▽ 6 ♡ 8",
"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 = abs(y * 2 / 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
Please fill your final a... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"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 = y + x + x + y。
和 ⊗，规则如下：
当y是3的倍数时，x ⊗ y = x - y ◎ 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 = 5 ◎ x - x ** y；
其他情况下，x ☆ y = 5 * (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: 2 % 3 ◎ 5 ☆ 8 ⊗ 1 * 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-320",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 % 3 ◎ 5 ☆ 8 ⊗ 1 * 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ♢, the rules are as follows:
when x and y are both odd, x ♢ y = abs(y * 2 + x) + x;
otherwise, x ♢ y = x * y - 2 * x.
and ⊙, the rules are as follows:
when the sum of x and y is even, x ⊙ y = 2 * x + y;
otherwise, x ⊙ y = y + (y - x) + x.
and △, the rules are as follows:
on the real number field, x △ y =... | {
"game_data": {
"answer": "784",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 8 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = (y - x) + y.
and ♡, the rules are as follows:
when x and y are both odd, x ♡ y = (x - y) / y;
otherwise, x ♡ y = 5 - y * x.
and △, the rules are as follows:
when x is greater than y, x △ y = (x ♡ x + y);
otherwise, x △ y = (x * x ♢ y).
The ... | {
"game_data": {
"answer": "49",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 4 △ 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 + y - y - x * y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 / 8 ▽ 2
Please fill y... | {
"game_data": {
"answer": "-0.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 / 8 ▽ 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：
当y是奇数时，x ♡ y = abs(4 * x * y)；
其他情况下，x ♡ y = x + x / y。
和 ▽，规则如下：
当y是5的倍数时，x ▽ y = y * x * y；
其他情况下，x ▽ y = x + y ♡ 5。
运算优先级：▽ > ** > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ▽ 4 ▽ 7 ♡ 5 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "303.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 4 ▽ 7 ♡ 5 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x + x * y + 4。
和 ♢，规则如下：
实数域上，x ♢ y = y + x - y + x。
和 ⊙，规则如下：
当y是5的倍数时，x ⊙ y = x ○ (x) * 2 - y；
其他情况下，x ⊙ y = (x) + x * y + x。
运算优先级：♢ > ⊙ > ** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ⊙ 10 + 2 ○ 2 ♢ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "52",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 10 + 2 ○ 2 ♢ 1",
"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 = abs(x * x) - y - y.
and △, the rules are as follows:
on the real number field, x △ y = y * y - 5 - x.
The precedence of operations: △ > ** > * = / = % = ☆ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses i... | {
"game_data": {
"answer": "5029",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 5 ☆ 5 △ 4",
"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 * 2 / y - y.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ○ 10 / 9
Please fill your... | {
"game_data": {
"answer": "-1.022222",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 10 / 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ⊙, the rules are as follows:
when x and y are both even, x ⊙ y = y + x - 3;
otherwise, x ⊙ y = x / y - 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 a multiple of 5, x ♡ y = abs(y) - x + x;
otherwise, x ♡ y = (x * y ** 2).
... | {
"game_data": {
"answer": "253",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 6 ⊙ 4",
"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 - x - y。
和 ♢，规则如下：
当y是奇数时，x ♢ y = (y ⊗ x * y + 5 * 3)；
其他情况下，x ♢ y = x + x / y。
和 ⊕，规则如下：
实数域上，x ⊕ y = abs(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: 8 ♢ 3 ⊕ 5 ⊗ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22.05",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 3 ⊕ 5 ⊗ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x / y + y.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ◇ 2
Please fill your final an... | {
"game_data": {
"answer": "4.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x - y + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y * y * x.
The precedence of operations: ** > * = / = % = ☆ > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "726",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 10 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y + x * x - y / x.
and △, the rules are as follows:
on the real number field, x △ y = x ◎ x * y - y * y.
The precedence of operations: ◎ > ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthese... | {
"game_data": {
"answer": "420",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 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 x is even, x ⊙ y = x ** x * y;
otherwise, x ⊙ y = y + x * x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x - y - y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x + y * x.
The precedence of operations: ♡ > ** > * = / = % = ⊙ >... | {
"game_data": {
"answer": "1397",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 8 ⊙ 6 ☆ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = (y * y + x - x) - y；
其他情况下，x ⊗ y = x - (x * y * y) / x。
和 ◎，规则如下：
实数域上，x ◎ y = y - y * x * y。
和 ♢，规则如下：
当x和y的和是偶数时，x ♢ y = 1 / x ⊗ y - y * y；
其他情况下，x ♢ y = 4 * y ◎ x。
运算优先级：♢ > ** = ⊗ = ◎ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ♢ 1 ◎ 6 % 10 ⊗ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-61",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 1 ◎ 6 % 10 ⊗ 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5的倍数时，x △ y = 5 - y + 1 - 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: 2 * 3 △ 2 ** 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "448",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 * 3 △ 2 ** 6",
"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 - 1 - x * 4 * y。
和 ▽，规则如下：
当y是偶数时，x ▽ y = y + x；
其他情况下，x ▽ y = y - 4 * 2 * 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 ♡ 5 ▽ 4 ▽ 7 % 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 5 ▽ 4 ▽ 7 % 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ◎, the rules are as follows:
when the sum of x and y is even, x ◎ y = y * y - x;
otherwise, x ◎ y = y + (y * x).
The precedence of operations: ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ex... | {
"game_data": {
"answer": "26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ⊕, the rules are as follows:
when x is less than y, x ⊕ y = x * x - y + x;
otherwise, x ⊕ y = 3 / abs(y + x) + y.
and ⊗, 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 equal to y, x ◇ y = y + x - y ⊕ y;
otherwise, x ◇ y = y * y + x.... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 2 ⊕ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y - abs(x) * 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 * x * y.
The precedence of operations: ** > * = / = % > + = - = □ = ☆ = ♢。
Pare... | {
"game_data": {
"answer": "-2878",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 1 ☆ 6 □ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 ▽，规则如下：
当y是3的倍数时，x ▽ y = x * x - y；
其他情况下，x ▽ y = x - y + y。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 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 / x。
和 ⊙，规则如下：
当x是5的倍数时，x ⊙ y = y + (y - x □ x) / y；
其他情况下，x ⊙ y = y * x + 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: 9 □ 6 * 8 % 3 ⊙ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 6 * 8 % 3 ⊙ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
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