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A chunk of symbols is a calculation [released]

# Challenge

Create a program that takes input of a string and outputs an integer using the following calculation system:

- The string can only contain `+`, `-`, `*`, `/`, `^`, `!` (or a different character; `!` is used here for demonstration), `(`, and `)`.
- In this system, a character shows the value of $1$. This demonstrates the value of an integer with the system. Examples are `+++++`, which is equal to `+ 5`, and `***`, which is `* 3`.
- Here are the operations of each symbol:
- - `+` is addition and for assigning a beginning positive integer. (`+++++++++` = `+ 9`)
- - `-` is subtraction and for assigning a beginning negative integer. (`-------------` = `-13`/`- 13`)
- - `*` is multiplication. (`**` = `* 2`)
- - `/` is division. (`//////` = `/ 6`)
- - `^` is exponentiation/ (`^^^` = `^ 3`)
- - `!` or a different character (I'm using `!` for demonstration) is for assigning positive integers if we want to add positive integers together, or to simply separate positive integers from each other.
- - `(` and `)` are for grouping calculations, and can also be used for multiplying a number into an equation. The only way to interact with the grouped equations is if no numbers precede them. `!!!+++++(----***)//` = `3 + 4(-4 * 3) / 2`)
- The output must be an integer, being the result of the whole equation.
- The whole system should follow [this non-standard model of PEMDAS](https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html).
- Being a <a class="badge is-tag">code-golf</a> challenge, the shortest program of each language wins.

# Testcases

- `+++++` is `+ 5` which returns `5`.
- `---**` is `-3 * 2` which returns `-6`.
- `++(----//+++++!!!**)` is `2(-4 / 2 + 5 + 3 * 2)` which returns `18` (`2(-2 + 5 + 6) => 2(9)`).
- `--^^^` is `-2 ^ 3` which returns `-8`.
- An empty input or `()` is `0` which returns `0`.
- `(+-)/(+-)` is `(1 - 1) / 1 (1 - 1)` is indeterminate, but for the sake of this challenge, it returns `0`.
- `(++++++++******)//((+++***)+++)` is `(8 * 6) / 2((3 * 3) + 3)` which returns `2` (`48 / 2(9 + 3) => 48 / 24`).

# Error Handling

Everything in this section is [undefined behavior](https://codegolf.codidact.com/comments/thread/3915#comment-12400). Please DON'T do these when inputting.

- A character that's not supposed to be there.
- A beginner number is assigned NOT by `+`, `-`, `!` (or a different character), or `(`.
- An open parentheses doesn't have a paired closed parentheses.
- A whitespace character in the string (tabs, spaces, etc.).
- Characters that aren't part of the English alphabet. `ñ`, `る` and `θ` are examples.
- An equation like `!/(+-)` or `1 / 1(1-1)` leads to the division by zero error. Refrain from doing such equations in the input. Only `0 / 0` is an exception here, which returns `0`.

# Suggestions

- Any way to improve this?
- Anything unclear?
- Are these the right tags?
- Any more errors to handle?

A chunk of symbols is a calculation

# Challenge

Create a program that takes input of a string and outputs an integer using the following calculation system:

- The string can only contain `+`, `-`, `*`, `/`, `^`, `(`, and `)`.
- In this system, a character shows the value of $1$. This demonstrates the value of an integer with the system. Examples are `+++++`, which is equal to `+ 5`, and `***`, which is `* 3`.
- Here are the operations of each symbol:
- - `+` is addition and for assigning a beginning positive integer. (`+++++++++` = `+ 9`)
- - `-` is subtraction and for assigning a beginning negative integer. (`-------------` = `-13`/`- 13`)
- - `*` is multiplication. (`**` = `* 2`)
- - `/` is division. (`//////` = `/ 6`)
- - `^` is exponentiation/ (`^^^` = `^ 3`)
- - `(` and `)` are for grouping calculations, and can also be used for multiplying a number into an equation. The only way to interact with the grouped equations is if no numbers precede them. `!!!+++++(----***)//` = `3 + 4(-4 * 3) / 2`)
- The output must be an integer, being the result of the whole equation.
- The whole system should follow GEMDAS (Grouping (Parentheses), Exponentiation, Multiplication/Division, Addition/Subtraction).
- Being a <a class="badge is-tag">code-golf</a> challenge, the shortest program of each language wins.

# Testcases

- `+++++` is `+ 5` which returns `5`.
- `---**` is `-4 * 2` which returns `-6`.
- `++(----//+++++++**)` is `2(-4 / 2 + 7 * 2)` which returns `24`.
- `--^^^` is `2 ^ 3` which returns `-8`.
- An empty input is `0` which returns `0`.

# Error Handling

Return a string to signify that the equation is invalid when:
- A character that's not supposed to be in the input is in the input.
- A beginner number is assigned NOT by `+`, `-`, or `(`.
- An open parentheses doesn't have a paired closed parentheses.

# Suggestions

- Any way to improve this?
- Anything unclear?
- Are these the right tags?
- Any more errors to handle?