




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





							'''simple docstring'''


							def is_in_circle(UpperCamelCase	:  float			,						UpperCamelCase	:  float				) -> bool:
														_a     					=    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
							_a     					=    mean(
							    int(is_in_circle(uniform(-1.0			,						1.0				)			,						uniform(-1.0			,						1.0				)				)				)
							    for _ in range(SCREAMING_SNAKE_CASE_				)				)
							# The ratio of the area for circle to square is pi/4.
							_a     					=    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_   (UpperCamelCase	:  int			,						UpperCamelCase	:  Callable[[float], float]			,						UpperCamelCase	:  float = 0.0			,						UpperCamelCase	:  float = 1.0			,						):





							'''simple docstring'''


							return mean(
							    function_to_integrate(uniform(SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_				)				) for _ in range(SCREAMING_SNAKE_CASE_				)				) * (max_value - min_value)
def 		snake_case_   (UpperCamelCase	:  int			,						UpperCamelCase	:  float = 0.0			,						UpperCamelCase	:  float = 1.0				):





							'''simple docstring'''


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

							_a     					=    area_under_curve_estimator(
							    SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_				)
							_a     					=    (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_   (UpperCamelCase	:  int				):





							'''simple docstring'''


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

							_a     					=    area_under_curve_estimator(
							    SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						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()







'''simple docstring'''


from __future__ import annotations
def 		snake_case_   (UpperCamelCase	:  list[int]				):





							'''simple docstring'''


							if not nums:
														return 0
							_a     					=    nums[0]
							_a     					=    0
							for num in nums[1:]:
														_a					,							_a     					=    (
														    max_excluding + num,
														    max(UpperCamelCase			,						UpperCamelCase				),
														)
							return max(UpperCamelCase			,						UpperCamelCase				)


if __name__ == "__main__":
				import doctest

				doctest.testmod()

