Evaluate Polynomials from String

You will be given a polynomial expression in string form. The expression will contain any of the following operations, written using standard mathematical notation for a single variable, "x", as illustrated in the examples below:

• addition: x + 1
• subtraction: x – 2
• multiplication: 3x
• division: x / 4
• exponentation: x^5
• brackets: x(x + 1)

Your task is to write a function that can evaluate such a polynomial for a given value of x. You will receive two arguments: the polynomial string and the input number.

If the mathematical expression contains an error, you should return "invalid".

Examples

evaluate_polynomial("x+1", 5) ➞ 6

evaluate_polynomial("5x^2", 3) ➞ 45

evaluate_polynomial("(x(x+1))/2", 4) ➞ 10

evaluate_polynomial("4(x + 3))/2", 5) ➞ "invalid"
# Invalid because parentheses not balanced.

Notes

The string will not contain spaces.