utils.py

import math


def fact(n):
    if n < 0:
        raise ValueError("must be positive")

    if n == 0:
        return 1

    result = 1

    for i in range(1, n + 1):
        result *= i

    return result


def roots(a, b, c):
    d = b**2 - 4 * a * c
    if d < 0:
        return ()
    else:
        roots = ((-b + math.sqrt(d)) / 2, (-b - math.sqrt(d)) / 2)
    return roots


def integrate(function, lower, upper):
    """Approximates the integral of a fonction between two bounds

    Pre: 'function' is a valid Python expression with x as a variable,
            'lower' <= 'upper',
            'function' continuous and integrable between 'lower‘ and 'upper'.
    Post: Returns an approximation of the integral from 'lower' to 'upper'
            of the specified 'function'.

    Hint: You can use the 'integrate' function of the module 'scipy' and
            you'll probably need the 'eval' function to evaluate the function
            to integrate given as a string.
    """
    pass


if __name__ == "__main__":
    print(fact(5))
    print(roots(1, 0, 1))
    print(integrate("x ** 2 - 1", -1, 1))