import math
from collections.abc import Callable


def intersection(function: Callable[[float], float], x0: float, x1: float) -> float:
 """
 function is the f we want to find its root
 x0 and x1 are two random starting points
 >>> intersection(lambda x: x ** 3 - 1, -5, 5)
 0.9999999999954654
 >>> intersection(lambda x: x ** 3 - 1, 5, 5)
 Traceback (most recent call last):
 ...
 ZeroDivisionError: float division by zero, could not find root
 >>> intersection(lambda x: x ** 3 - 1, 100, 200)
 1.0000000000003888
 >>> intersection(lambda x: x ** 2 - 4 * x + 3, 0, 2)
 0.9999999998088019
 >>> intersection(lambda x: x ** 2 - 4 * x + 3, 2, 4)
 2.9999999998088023
 >>> intersection(lambda x: x ** 2 - 4 * x + 3, 4, 1000)
 3.0000000001786042
 >>> intersection(math.sin, -math.pi, math.pi)
 0.0
 >>> intersection(math.cos, -math.pi, math.pi)
 Traceback (most recent call last):
 ...
 ZeroDivisionError: float division by zero, could not find root
 """
 x_n: float = x0
 x_n1: float = x1
 while True:
 if x_n == x_n1 or function(x_n1) == function(x_n):
 raise ZeroDivisionError("float division by zero, could not find root")
 x_n2: float = x_n1 - (
 function(x_n1) / ((function(x_n1) - function(x_n)) / (x_n1 - x_n))
 )
 if abs(x_n2 - x_n1) < 10**-5:
 return x_n2
 x_n = x_n1
 x_n1 = x_n2


def f(x: float) -> float:
 return math.pow(x, 3) - (2 * x) - 5


if __name__ == "__main__":
 print(intersection(f, 3, 3.5))