






from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean
def 					snake_case_						(   lowerCAmelCase_				:  int					):

							# A local function to see if a dot lands in the circle.
							def is_in_circle(lowerCAmelCase_				:  float				,				lowerCAmelCase_				:  float					) -> bool:
														__lowercase					:							List[Any]			=   sqrt((x**2) + (y**2)					)
														# Our circle has a radius of 1, so a distance
														# greater than 1 would land outside the circle.
														return distance_from_centre <= 1

							# The proportion of guesses that landed in the circle
							__lowercase					:							Tuple			=   mean(
							    int(is_in_circle(uniform(-1.0				,				1.0					)				,				uniform(-1.0				,				1.0					)					)					)
							    for _ in range(lowerCAmelCase_					)					)
							# The ratio of the area for circle to square is pi/4.
							__lowercase					:							Union[str, Any]			=   proportion * 4
							print(F"The estimated value of pi is {pi_estimate}"					)
							print(F"The numpy value of pi is {pi}"					)
							print(F"The total error is {abs(pi - pi_estimate					)}"					)
def 					snake_case_						(   lowerCAmelCase_				:  int				,				lowerCAmelCase_				:  Callable[[float], float]				,				lowerCAmelCase_				:  float = 0.0				,				lowerCAmelCase_				:  float = 1.0				,				):
							return mean(
							    function_to_integrate(uniform(lowerCAmelCase_				,				lowerCAmelCase_					)					) for _ in range(lowerCAmelCase_					)					) * (max_value - min_value)
def 					snake_case_						(   lowerCAmelCase_				:  int				,				lowerCAmelCase_				:  float = 0.0				,				lowerCAmelCase_				:  float = 1.0					):

							def identity_function(lowerCAmelCase_				:  float					) -> float:
														return x

							__lowercase					:							int			=   area_under_curve_estimator(
							    lowerCAmelCase_				,				lowerCAmelCase_				,				lowerCAmelCase_				,				lowerCAmelCase_					)
							__lowercase					:							Tuple			=   (max_value * max_value - min_value * min_value) / 2

							print("""******************"""					)
							print(F"Estimating area under y=x where x varies from {min_value} to {max_value}"					)
							print(F"Estimated value is {estimated_value}"					)
							print(F"Expected value is {expected_value}"					)
							print(F"Total error is {abs(estimated_value - expected_value					)}"					)
							print("""******************"""					)
def 					snake_case_						(   lowerCAmelCase_				:  int					):

							def function_to_integrate(lowerCAmelCase_				:  float					) -> float:
														return sqrt(4.0 - x * x					)

							__lowercase					:							int			=   area_under_curve_estimator(
							    lowerCAmelCase_				,				lowerCAmelCase_				,				0.0				,				2.0					)

							print("""******************"""					)
							print("""Estimating pi using area_under_curve_estimator"""					)
							print(F"Estimated value is {estimated_value}"					)
							print(F"Expected value is {pi}"					)
							print(F"Total error is {abs(estimated_value - pi					)}"					)
							print("""******************"""					)


if __name__ == "__main__":
	import doctest

	doctest.testmod()







import math
def 					snake_case_						(   lowerCAmelCase_				:  int					):

							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(lowerCAmelCase_					) + 1					)				,				6					):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True
def 					snake_case_						(   lowerCAmelCase_				:  int = 10001					):

							try:
														__lowercase					:							Optional[int]			=   int(lowerCAmelCase_					)
							except (TypeError, ValueError):
														raise TypeError("""Parameter nth must be int or castable to int."""					) from None
							if nth <= 0:
														raise ValueError("""Parameter nth must be greater than or equal to one."""					)
							__lowercase					:							list[int]			=   []
							__lowercase					:							str			=   2
							while len(lowerCAmelCase_					) < nth:
														if is_prime(lowerCAmelCase_					):
																					primes.append(lowerCAmelCase_					)
																					num += 1
														else:
																					num += 1
							return primes[len(lowerCAmelCase_					) - 1]


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