
from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean



def 						lowercase_      (       A__		)							->							Dict:
    """simple docstring"""

    def is_in_circle(A__			,		A__		) -> bool:
        snake_case								= 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
    snake_case								= 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.
    snake_case								= 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 						lowercase_      (       A__			,		A__			,		A__ = 0.0			,		A__ = 1.0			,		)							->							List[Any]:
    """simple docstring"""

    return mean(
        function_to_integrate(uniform(lowerCAmelCase__			,		lowerCAmelCase__		)		) for _ in range(lowerCAmelCase__		)		) * (max_value - min_value)



def 						lowercase_      (       A__			,		A__ = 0.0			,		A__ = 1.0		)							->							str:
    """simple docstring"""

    def identity_function(A__		) -> float:
        return x

    snake_case								= area_under_curve_estimator(
        lowerCAmelCase__			,		lowerCAmelCase__			,		lowerCAmelCase__			,		lowerCAmelCase__		)
    snake_case								= (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 						lowercase_      (       A__		)							->							Any:
    """simple docstring"""

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

    snake_case								= 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()



class 					lowerCamelCase		:





     def __init__(self				:   List[Any]    ,   _A				:   str       )						->						Any:
         # we need a list not a string, so do something to change the type
         snake_case								= arr.split(","       )





     def 		UpperCAmelCase(self				:   str       )						->						str:
         snake_case								= [int(self.array[0]       )] * len(self.array       )
         snake_case								= [int(self.array[0]       )] * len(self.array       )
         for i in range(1    ,   len(self.array       )       ):
             snake_case								= max(
                 int(self.array[i]       ) + sum_value[i - 1]    ,   int(self.array[i]       )       )
             snake_case								= max(sum_value[i]    ,   rear[i - 1]       )
         return rear[len(self.array       ) - 1]


if __name__ == "__main__":
   _A   =			input("please input some numbers:")
   _A   =			SubArray(whole_array)
   _A   =			array.solve_sub_array()
   print(("the results is:", re))

