env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = y - y + y + x;
otherwise, x ◇ y = x - y + abs(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 = 3 + y * 4 - x + 1.
The precedence of operation... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 2 ☆ 3 ◇ 8",
"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 / 5 - 2。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ○ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x + 5 / y * x。
和 ☆，规则如下：
实数域上，x ☆ y = x ♢ x - x + y * 4。
和 ▽，规则如下：
当x大于y时，x ▽ y = y ** x + y + y * x；
其他情况下，x ▽ y = x * y + (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: 1 ☆ 4 ♢ 2 ▽ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "297",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 4 ♢ 2 ▽ 4",
"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的和是奇数时，x ♢ y = x * y + 1；
其他情况下，x ♢ y = (x - y / y)。
和 ⊕，规则如下：
实数域上，x ⊕ y = 4 * (y) - x。
和 ♡，规则如下：
当y是偶数时，x ♡ y = y - x + 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: 6 ♢ 10 ⊕ 3 ♡ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 10 ⊕ 3 ♡ 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等于y时，x ⊕ y = abs(5 * y) + x；
其他情况下，x ⊕ y = y / (3) / x。
和 ◎，规则如下：
实数域上，x ◎ y = x * y + x。
和 △，规则如下：
实数域上，x △ y = x ◎ 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 ⊕ 4 △ 10 ◎ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "66.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 4 △ 10 ◎ 1",
"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 - 3 + (y + y / y)。
和 □，规则如下：
实数域上，x □ y = y * (y - 3) * x。
和 ◎，规则如下：
实数域上，x ◎ y = y * y + x。
运算优先级：□ > ** = ⊕ > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 □ 10 ◎ 6 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "361",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 10 ◎ 6 ⊕ 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 - x - y。
和 ○，规则如下：
实数域上，x ○ y = x - x - 1 - y。
和 ▽，规则如下：
实数域上，x ▽ y = y + y + y + x。
运算优先级：⊕ = ○ > ** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ⊕ 1 ○ 9 ▽ 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 ⊕ 1 ○ 9 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * y * 1。
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 ◎ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "900",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 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.
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 / 1 △ 10
Please fill your final a... | {
"game_data": {
"answer": "0.454545",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 / 1 △ 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大于y时，x ◎ y = y ** x * x - 5；
其他情况下，x ◎ y = y * 1 + x * x。
和 ⊗，规则如下：
当x是3的倍数时，x ⊗ y = y * x ◎ 1；
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: 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 | Define ○, 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 expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ○ 3 % 10 ** 9
Please fill... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 3 % 10 ** 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y + 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: 10 * 1 △ 8
Please fill yo... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 * 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 + (x - x) + y / y。
和 ⊕，规则如下：
实数域上，x ⊕ y = y * 5 + x ◎ y。
和 ♡，规则如下：
当x和y都是偶数时，x ♡ y = abs(y - x / y) + 3；
其他情况下，x ♡ y = (4 - x ◎ y) - x。
运算优先级：♡ > ** = ◎ > * = / = % > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ♡ 7 ⊕ 1 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 7 ⊕ 1 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ◎，规则如下：
当x等于y时，x ◎ y = y - x + y - 1 / x；
其他情况下，x ◎ y = y * 4 - x。
和 ⊙，规则如下：
当x和y都是奇数时，x ⊙ y = x * x - y * y ◎ x；
其他情况下，x ⊙ y = (x + y / x) * y * y。
运算优先级：⊙ > ** > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ◎ 3 ⊙ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "52.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 3 ⊙ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ▽, the rules are as follows:
when x is odd, x ▽ y = x * x ** y - x * x;
otherwise, x ▽ y = y ** x - x + y - y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expr... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ◇，规则如下：
当x和y都是偶数时，x ◇ y = abs(4 * x) - y；
其他情况下，x ◇ y = y * x ** y。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 - 5 % 7 ◇ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 - 5 % 7 ◇ 10",
"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 * abs(x) - y.
and ○, the rules are as follows:
on the real number field, x ○ y = abs(y) / x.
and □, the rules are as follows:
when x is less than y, x □ y = abs(x - y + y);
otherwise, x □ y = (y ** x) * y.
The precedence of operations: ** =... | {
"game_data": {
"answer": "12.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 4 □ 2 ⊗ 7",
"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和y都是奇数时，x ♢ y = x + y - x；
其他情况下，x ♢ y = x * y * 3。
和 ♡，规则如下：
实数域上，x ♡ y = x + (x * y)。
和 ▽，规则如下：
当x大于y时，x ▽ y = x + 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: 5 ♢ 5 ▽ 10 ♡ 10 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "222",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 5 ▽ 10 ♡ 10 ▽ 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 even, x ☆ y = x + y + y * x / x;
otherwise, x ☆ y = y - y * x * y + x.
and ○, the rules are as follows:
when x is a multiple of 3, x ○ y = y - y * x + x - y;
otherwise, x ○ y = 5 * 2 ☆ x + y * 2.
The precedence of operations: ○ > ** > * = / = % = ☆ > + =... | {
"game_data": {
"answer": "-309",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 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x和y的和是偶数时，x □ y = y - x * y * y - y；
其他情况下，x □ y = 4 + y - x / y / x。
和 ◇，规则如下：
实数域上，x ◇ y = x + (x * y ** x + x)。
运算优先级：◇ > ** > * = / = % = □ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 □ 2 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-360",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 2 ◇ 1",
"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) + y - x。
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 = y * y + x。
运算优先级：☆ > ** > * = / = % > + = - = ⊗ = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ⊗ 7 ♡ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 7 ♡ 3",
"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y是奇数时，x ○ y = (x - x + y) + y；
其他情况下，x ○ y = y * y - x。
和 ♢，规则如下：
当y是3的倍数时，x ♢ y = (y ○ x - x)；
其他情况下，x ♢ y = abs(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 ○ 3 ♢ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4.222222",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 3 ♢ 2",
"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 = 2 * x - y - 2；
其他情况下，x ⊕ y = 4 + 3 * x - y。
和 ⊙，规则如下：
实数域上，x ⊙ y = (y) ⊕ x。
和 ⊗，规则如下：
实数域上，x ⊗ y = y + x / x * x。
运算优先级：⊕ = ⊙ > ** = ⊗ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊙ 3 ⊗ 3 ⊕ 5 - 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 3 ⊗ 3 ⊕ 5 - 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y / 4 * x.
and △, the rules are as follows:
on the real number field, x △ y = (x * x) * y * y.
The precedence of operations: △ > ** > * = / = % > + = - = □。
Parentheses have the highest priority, and the expression inside the parentheses is calcu... | {
"game_data": {
"answer": "720",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 6 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ⊕, the rules are as follows:
when x is a multiple of 5, x ⊕ y = x - 2 + x - abs(2 + y);
otherwise, x ⊕ y = x * y - x - x + y.
and □, the rules are as follows:
when x and y are both even, x □ y = y - (y ⊕ x / x);
otherwise, x □ y = x + y.
and ☆, the rules are as follows:
when y is a multiple of 3, x ☆ y =... | {
"game_data": {
"answer": "-22.571429",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊕ 1 ☆ 2 □ 2",
"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 = 4 + y + y + x。
和 △，规则如下：
当x和y都是奇数时，x △ y = (y ♡ x) * x * y；
其他情况下，x △ y = y + x - x ♡ x。
运算优先级：** > * = / = % = △ > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 △ 6 ♡ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "28",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 6 ♡ 1",
"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 even, x □ y = y ** x;
otherwise, x □ y = abs(x) + y.
and ♢, the rules are as follows:
when the sum of x and y is even, x ♢ y = x □ y + 2;
otherwise, x ♢ y = x * y * y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + y / y.
The precedence of ... | {
"game_data": {
"answer": "1.363636",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 / 3 □ 8 ⊗ 6 ♢ 4",
"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 = abs(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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = 5 - y / x + 1。
和 ☆，规则如下：
实数域上，x ☆ y = x □ y。
运算优先级：☆ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 □ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 7",
"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 + x - y + x；
其他情况下，x ○ y = 5 - 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: 8 ○ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12",
"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 + 5 + 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 calculate... | {
"game_data": {
"answer": "34",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 10 ☆ 1",
"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 + x。
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 = 5 + (x * y - 4)；
其他情况下，x ◎ y = 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: 9 ◎ 10 ♡ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.043956",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 10 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ♡，规则如下：
当y是偶数时，x ♡ y = (y - x + x)；
其他情况下，x ♡ y = x + y - y。
和 ⊕，规则如下：
当x大于y时，x ⊕ y = x - x - y；
其他情况下，x ⊕ y = 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: 1 ♡ 7 ** 3 * 8 ⊕ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 7 ** 3 * 8 ⊕ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ○，规则如下：
当y是5的倍数时，x ○ y = y - y - abs(x) - x - x；
其他情况下，x ○ y = (x ** x + x + x - y)。
和 ▽，规则如下：
当x和y都是偶数时，x ▽ y = x + x ○ y / x；
其他情况下，x ▽ y = x + y - y / y - y。
和 ♢，规则如下：
实数域上，x ♢ y = x ** x + x ○ y - y。
运算优先级：♢ > ○ > ** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 % 1 ○ 5 ♢ 5 ▽ 3
请将最终答案填入\bo... | {
"game_data": {
"answer": "-3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 % 1 ○ 5 ♢ 5 ▽ 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 x and y are both even, x ♢ y = x * 5 * y + x - 2;
otherwise, 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 e... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 % 7 ♢ 10",
"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 a multiple of 3, x ○ y = y ** x * abs(3) - y;
otherwise, x ○ y = x + 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 ... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 2 + 1",
"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 = x + abs(y - x + y).
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ▽ 9
Please fill your... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ⊗，规则如下：
当x是5的倍数时，x ⊗ y = y * 3 - x；
其他情况下，x ⊗ y = y - y - x / 1。
运算优先级：** > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 % 7 ⊗ 3 / 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 % 7 ⊗ 3 / 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ☆，规则如下：
当x是奇数时，x ☆ y = y - y * x；
其他情况下，x ☆ y = y + (x * y)。
和 ⊙，规则如下：
当x是奇数时，x ⊙ y = y - (x * 3)；
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: 9 ☆ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 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 * 4 * 2 * 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: 8
Please fill your fin... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"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:
on the real number field, x ⊗ y = x * abs(y * y).
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x / y ** 1.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x + x * y.
The precedence of operations: ⊙ = ▽ > ** > * = / = % > + = - = ⊗。
Paren... | {
"game_data": {
"answer": "39.506173",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 4 ▽ 4 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": 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 - x.
and ◎, the rules are as follows:
when x is odd, x ◎ y = x + 3 ☆ y;
otherwise, x ◎ y = y * y + x.
The precedence of operations: ** > * = / = % > + = - = ☆ = ◎。
Parentheses have the highest priority, an... | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y + x - x。
和 ⊗，规则如下：
当x和y都是偶数时，x ⊗ y = 5 ⊕ y + y * x；
其他情况下，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 / 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 □ 8 ⊕ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 □ 8 ⊕ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊗, the rules are as follows:
when y is even, x ⊗ y = x / y ** y * x;
otherwise, x ⊗ y = y * x - x + y.
and ○, the rules are as follows:
on the real number field, x ○ y = y - y ⊗ (x) * x.
and ♢, the rules are as follows:
when y is even, x ♢ y = (x ** y + y) + x;
otherwise, x ♢ y = y / y * x ○ (x).
The p... | {
"game_data": {
"answer": "-1071",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 8 ○ 2 ⊗ 10 - 2 ⊗ 1",
"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 - 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 expression: 6 ◇ 5
Please fill your... | {
"game_data": {
"answer": "-12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 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 is a multiple of 5, x ⊙ y = x - (y) / y;
otherwise, x ⊙ y = x * x * y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = 2 + y * x.
and ○, the rules are as follows:
on the real number field, x ○ y = x + x - y.
The precedence of operations: ⊙ > ○ > ** >... | {
"game_data": {
"answer": "2514",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 10 ○ 6 ⊗ 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 = x + y + y;
otherwise, x ▽ y = y + (y - x + y).
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expr... | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 10 - 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:
when y is odd, x ♡ y = x + x + y - x / 1;
otherwise, x ♡ y = x + y - x.
and ○, the rules are as follows:
when x is greater than y, x ○ y = y - x * y / y + y;
otherwise, x ○ y = y - y - x ** (x + x).
The precedence of operations: ○ > ** > * = / = % > + = - = ♡。
Parentheses hav... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 6 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y + 1 + x.
and ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = (y ⊙ x) * y;
otherwise, x ◎ y = 1 + abs(y * x).
and □, the rules are as follows:
when y is a multiple of 3, x □ y = x * y;
otherwise, x □ y = y ⊙ x.
The pre... | {
"game_data": {
"answer": "145",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 3 □ 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:
when x is equal to y, x ⊕ y = x + x / y - y * 4;
otherwise, x ⊕ y = x - x - y ** y * y.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = x + (3 * 3) - y * 3;
otherwise, x ♡ y = y + y + x + 3 + x.
and ○, the rules are as follows:
when x is a multiple of... | {
"game_data": {
"answer": "0.000129",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 8 ⊕ 9 ♡ 8",
"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。
和 ⊕，规则如下：
当x和y的和是奇数时，x ⊕ y = x + y - x + x - (y)；
其他情况下，x ⊕ y = 5 + x / x ♡ x * y。
运算优先级：** > * = / = % > + = - = ♡ = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 / 4 ⊕ 3 ** 1 ♡ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 / 4 ⊕ 3 ** 1 ♡ 3",
"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 a multiple of 5, x ○ y = y + 1 + x;
otherwise, 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... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = abs(x) - y - x ** y.
and ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = x + y ** y - 4;
otherwise, x ⊙ y = (x / y - y).
and ◎, the rules are as follows:
on the real number field, x ◎ y = y + y + x / y.
The precedence of opera... | {
"game_data": {
"answer": "-3869.252553",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 1 ⊙ 9 ⊗ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ⊗，规则如下：
当x和y的和是奇数时，x ⊗ y = x + y - y + x * x；
其他情况下，x ⊗ y = y + 5 * y * 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 = 4 ⊗ y + x + y + x；
其他情况下，x ♢ y = x ⊗ 4 + 2 * 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 ⊙ 3 ♢ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "42",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 3 ♢ 10",
"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 * y + y.
and ⊕, the rules are as follows:
when the sum of x and y is even, x ⊕ y = x ☆ x - x + y;
otherwise, x ⊕ y = y + x ** y / y.
The precedence of operations: ** > * = / = % = ☆ > + = - = ⊕。
Parentheses have the highest priority, and the ... | {
"game_data": {
"answer": "24",
"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:
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: 7 + 10 ▽ 1
Please fill your fin... | {
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"expression": "7 + 10 ▽ 1",
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"full_sequence": null,
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logic-v2 | 定义 ♡，规则如下：
当x是偶数时，x ♡ y = x / y；
其他情况下，x ♡ y = x + y - y。
和 ☆，规则如下：
实数域上，x ☆ y = x + y - abs(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 ☆ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
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"closing_sequence": null,
"expression": "9 ♡ 9 ☆ 3",
"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 and y are both odd, x △ y = x * x * y + x + x;
otherwise, x △ y = y + y * (y - x + y).
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value... | {
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"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 1 % 8 * 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ◇，规则如下：
当y是3的倍数时，x ◇ y = y - (x * y - y) * y；
其他情况下，x ◇ y = 4 - 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 - 1
请将最终答案填入\boxed{}中。 | {
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"answer": "-7",
"difficulty": 1,
"gpt_response": "",
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"expression": "2 ◇ 3 - 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是奇数时，x △ y = x + y / 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: 4 ** 1 △ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ** 1 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊙，规则如下：
当x是偶数时，x ⊙ y = y + y - x；
其他情况下，x ⊙ y = x + x * y。
和 ○，规则如下：
当y是3的倍数时，x ○ y = (x ⊙ y) + 2 - y；
其他情况下，x ○ y = (x * y ⊙ y)。
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: 2 △ 7 ○ 7 ⊙ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4802",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 7 ○ 7 ⊙ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ⊗，规则如下：
当x是奇数时，x ⊗ y = 1 + x * y；
其他情况下，x ⊗ y = (y - 3) * x。
和 ⊕，规则如下：
当x小于y时，x ⊕ y = abs(y - y) - x；
其他情况下，x ⊕ y = x * y * x。
和 ⊙，规则如下：
当x是奇数时，x ⊙ y = x / y - y；
其他情况下，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: 2 ⊗ 7 ⊙ 4 ⊕ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "330.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 7 ⊙ 4 ⊕ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = x - 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 = x + x ○ y + y.
The precedence of operations: ○ = ⊙ > ** = ◇ > * = / = % > + = -。
Parenth... | {
"game_data": {
"answer": "-6.3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 5 ◇ 9 ⊙ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y * x - 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: 6 △ 1
请将最终答案填入\boxed{}中。 | {
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"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ♡，规则如下：
当y是3的倍数时，x ♡ y = (y - y / x)；
其他情况下，x ♡ y = 1 + y + x。
和 ☆，规则如下：
实数域上，x ☆ y = x - x * y。
运算优先级：♡ > ☆ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 7 ☆ 4 ** 1 * 7
请将最终答案填入\boxed{}中。 | {
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"answer": "-189",
"difficulty": 1,
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"metadata": {
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"expression": "1 ♡ 7 ☆ 4 ** 1 * 7",
"fill_length": null,
"full_sequence": null,
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"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 ◎，规则如下：
当x和y的和是偶数时，x ◎ y = x - (y * y) * x；
其他情况下，x ◎ y = y - 4 + x - 4 - 2。
和 ⊗，规则如下：
实数域上，x ⊗ y = y * 2 + 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: 6 + 6 / 8 ⊗ 2 ◎ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5.996703",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 + 6 / 8 ⊗ 2 ◎ 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 * y - y + x.
and □, the rules are as follows:
when the sum of x and y is even, x □ y = y ** x + 2 ** 3 + 5;
otherwise, x □ y = x + y * x - y.
The precedence of operations: ** = ⊙ = □ > * = / = % > + = -。
Parentheses have the highest priority,... | {
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"answer": "61",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 6 ⊙ 4",
"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 = (y + 1 + x)。
和 ▽，规则如下：
实数域上，x ▽ y = y ◎ y - x。
运算优先级：◎ = ▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 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 = y - y - x * x + y。
和 △，规则如下：
当x等于y时，x △ y = x - y / y / x ⊗ y；
其他情况下，x △ y = y - y ⊗ x - x * x。
和 □，规则如下：
实数域上，x □ y = x / 5 ⊗ y + 2。
运算优先级：⊗ > ** = △ > * = / = % > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊗ 8 △ 3 □ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.421053",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 8 △ 3 □ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = (y + 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 ▽ 2 ▽ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "45",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 2 ▽ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ○, the rules are as follows:
when x is odd, x ○ y = y * y - x;
otherwise, x ○ y = x + x + 2 - y.
and ◇, the rules are as follows:
when y is odd, x ◇ y = x * x / (x) + y;
otherwise, x ◇ y = y * x + x - y.
and △, the rules are as follows:
on the real number field, x △ y = x / x + y.
The precedence of ope... | {
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"answer": "6",
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"gpt_response": "",
"metadata": {
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"expression": "2 ◇ 4 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 △，规则如下：
当x和y都是偶数时，x △ y = x - y * y；
其他情况下，x △ y = y - y + x。
和 ♡，规则如下：
当x和y的和是偶数时，x ♡ y = x * y △ y；
其他情况下，x ♡ y = x + y ** 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 ♡ 3 ** 10
请将最终答案填入\boxed{}中。 | {
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"answer": "59049",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 5 ♡ 3 ** 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x * y + y - y。
和 △，规则如下：
实数域上，x △ y = x - x / x ** y。
和 ◎，规则如下：
当x是3的倍数时，x ◎ y = y * y - x - x；
其他情况下，x ◎ y = y + x + 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: 7 △ 1 ♢ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6.997085",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 1 ♢ 4",
"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 = abs(y * x)。
和 ♢，规则如下：
实数域上，x ♢ y = x ♡ y * (1 - y)。
和 △，规则如下：
当x是5的倍数时，x △ y = x ♢ y - (1 + 5)；
其他情况下，x △ y = x ♡ y。
运算优先级：♡ = △ > ** = ♢ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ♡ 1 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 1 △ 5",
"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 / y / x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x ♢ y.
and ⊗, the rules are as follows:
when y is even, x ⊗ y = x + y;
otherwise, x ⊗ y = x * 4 - y.
The precedence of operations: ⊗ > ** > * = / = % = ♢ = ▽ > + = ... | {
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"answer": "0.111111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 4 ▽ 6 ♢ 7 ⊗ 9",
"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.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ▽ 1 + 9
Please fill your final an... | {
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"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 1 + 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ▽，规则如下：
当x和y都是偶数时，x ▽ y = (y + x) * x；
其他情况下，x ▽ y = x + (y + y * y)。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ▽ 6 ▽ 2 + 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "65",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 6 ▽ 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：
实数域上，x ♢ y = x + y * x。
和 ▽，规则如下：
实数域上，x ▽ y = x * abs(y - y) - 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: 7 △ 4 ▽ 2 - 6 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-38",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 4 ▽ 2 - 6 ♢ 5",
"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 a multiple of 3, x ◇ y = 1 - y + x + x;
otherwise, x ◇ y = 1 + 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": "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 = x + 4 - x / 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 ◇ 7 * 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "46.428571",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 7 * 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y / x * y。
和 ☆，规则如下：
当x大于y时，x ☆ y = abs(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) * 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 ♢ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 5 ♢ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ▽，规则如下：
当y是奇数时，x ▽ y = 4 - 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: 4 / 3 ▽ 8 ** 10
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 / 3 ▽ 8 ** 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y - abs(x + x) / y.
and ⊕, the rules are as follows:
when x is less than y, x ⊕ y = y - y ◇ x;
otherwise, x ⊕ y = 4 * x * y ◇ 3.
and △, the rules are as follows:
on the real number field, x △ y = (y ** x * 1).
The precedence of operations: △ ... | {
"game_data": {
"answer": "37.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 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:
on the real number field, x ☆ y = y + (y * y - x).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + y ** 4.
The precedence of operations: ☆ > ** > * = / = % > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calc... | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 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 = x + y / x.
and ○, the rules are as follows:
when x is greater than y, x ○ y = x + y;
otherwise, x ○ y = y - x - x.
The precedence of operations: □ = ○ > ** > * = / ... | {
"game_data": {
"answer": "-6.142857",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 4 ○ 9 ♢ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = (y + y + x - x ** 1).
and ▽, the rules are as follows:
on the real number field, x ▽ y = 3 * 2 * 4 - x - y.
The precedence of operations: ▽ > ** > * = / = % > + = - = ◎。
Parentheses have the highest priority, and the expression inside the parenth... | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = 1 - x + x / y - 1.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + y * 1.
The precedence of operations: ☆ = ⊕ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "3787.995116",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ** 2 ☆ 4 ⊕ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ♢, the rules are as follows:
when the sum of x and y is even, x ♢ y = y + x * x;
otherwise, x ♢ y = x + y - 4.
and ▽, the rules are as follows:
when the sum of x and y is odd, x ▽ y = abs(y * x / x);
otherwise, x ▽ y = 3 / (y ♢ x).
The precedence of operations: ** = ♢ = ▽ > * = / = % > + = -。
Parentheses... | {
"game_data": {
"answer": "-70.285714",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 1 ▽ 5 - 8 ♢ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = 1 + 5 + 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: 5 ○ 3 % 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 3 % 7",
"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和y的和是偶数时，x △ y = (y - y) - x；
其他情况下，x △ y = y + (x - x)。
和 ○，规则如下：
当y是3的倍数时，x ○ y = x + y * x；
其他情况下，x ○ y = x * y + 1。
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 ☆ 10 - 6 △ 7 △ 10 ○ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-85",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ☆ 10 - 6 △ 7 △ 10 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ♢，规则如下：
当x是偶数时，x ♢ y = x + abs(y + y)；
其他情况下，x ♢ y = x + y。
和 ◇，规则如下：
实数域上，x ◇ y = x * x / y。
和 ⊙，规则如下：
实数域上，x ⊙ y = x * 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 ◇ 1 ♢ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 4 ◇ 1 ♢ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define △, the rules are as follows:
when x is even, x △ y = y + x - y - y * x;
otherwise, x △ y = y + 2 ** 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 expr... | {
"game_data": {
"answer": "0.583333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 / 3 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x + y * x / x * y。
和 ☆，规则如下：
当y是3的倍数时，x ☆ y = y / x + y - y + y；
其他情况下，x ☆ y = x / y ◎ 1 * 5。
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: 2 ♡ 3 / 9 ♡ 10 ◎ 6 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "400.05618",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 3 / 9 ♡ 10 ◎ 6 ☆ 2",
"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 = 1 + 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 ▽ 2 + 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 2 + 2",
"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 + 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 a multiple of 3, x ▽ y = (x + x * y);
otherwise, x ▽ y = x - x - y.
The precedence of operations: ⊕ = △ = ▽ ... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 6 ▽ 1 ⊕ 1 * 4",
"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 = y * x + y * x + x；
其他情况下，x ⊙ y = y * x * x + y - x。
和 ◎，规则如下：
实数域上，x ◎ y = y - y ⊙ (3 - 2) * x。
和 ▽，规则如下：
实数域上，x ▽ y = y * (x + 4) - 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: 7 ⊙ 8 ◎ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-22393",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 8 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊙，规则如下：
当x是偶数时，x ⊙ y = y * x；
其他情况下，x ⊙ y = x * x - y。
和 ○，规则如下：
当y是偶数时，x ○ y = y ** x + y；
其他情况下，x ○ y = 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: 1 ⊙ 4 ○ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4.015625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 4 ○ 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 y is a multiple of 3, x ⊗ y = x * x * x - y;
otherwise, x ⊗ y = x + y ** 2 + y - x.
and ◎, 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 + 4 + 2) + y / 2.
The preceden... | {
"game_data": {
"answer": "79",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊙ 5 ◎ 3 ⊗ 8 ⊙ 2",
"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。
和 ▽，规则如下：
实数域上，x ▽ y = x * y。
和 ♡，规则如下：
当x和y的和是偶数时，x ♡ y = y ** x * 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: 2 ▽ 1 ♡ 8 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "519",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 1 ♡ 8 ⊕ 7",
"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 - x * 5。
和 △，规则如下：
实数域上，x △ y = (x - x - x) * y + y。
运算优先级：△ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ◎ 10 △ 5 + 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-83",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 10 △ 5 + 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
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