
from collections.abc import Callable




def 				a						(							snake_case__:					Callable[[float], float]						,   snake_case__:					float						,   snake_case__:					float					):


				'''simple docstring'''
				lowercase_       =					a
				lowercase_       =					b
				if function(snake_case__					) == 0:  # one of the a or b is a root for the function
								return a
				elif function(snake_case__					) == 0:
								return b
				elif (
				    function(snake_case__					) * function(snake_case__					) > 0
				):  # if none of these are root and they are both positive or negative,
								# then this algorithm can't find the root
								raise ValueError('''could not find root in given interval.'''					)
				else:
								lowercase_       =					start + (end - start) / 2.0
								while abs(start - mid					) > 10**-7:  # until precisely equals to 10^-7
												if function(snake_case__					) == 0:
																return mid
												elif function(snake_case__					) * function(snake_case__					) < 0:
																lowercase_       =					mid
												else:
																lowercase_       =					mid
												lowercase_       =					start + (end - start) / 2.0
								return mid




def 				a						(							snake_case__:					float					):


				'''simple docstring'''
				return x**3 - 2 * x - 5


if __name__ == "__main__":
						print(bisection(f, 1, 1_0_0_0))

						import doctest

						doctest.testmod()






import itertools
import math




def 				a						(							snake_case__:					int					):


				'''simple docstring'''

				if 1 < number < 4:
								# 2 and 3 are primes
								return True
				elif number < 2 or number % 2 == 0 or number % 3 == 0:
								# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
								return False

				# All primes number are in format of 6k +/- 1
				for i in range(5						,   int(math.sqrt(snake_case__					) + 1					)						,   6					):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True




def 				a						(							):


				'''simple docstring'''
				lowercase_       =					2
				while True:
								if is_prime(snake_case__					):
												yield num
								num += 1




def 				a						(							snake_case__:					int = 10_001					):


				'''simple docstring'''
				return next(itertools.islice(prime_generator()						,   nth - 1						,   snake_case__					)					)


if __name__ == "__main__":
						print(f"{solution() = }")




