



def       A_   (						__a  :					Dict			,		__a  :					int		):

				"""simple docstring"""
				# "Simpson Rule"
				# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
				a__					   =		(boundary[1] - boundary[0]) / steps
				a__					   =		boundary[0]
				a__					   =		boundary[1]
				a__					   =		make_points(__a			,		__a			,		__a		)
				a__					   =		0.0
				y += (h / 3.0) * f(__a		)
				a__					   =		2
				for i in x_i:
								y += (h / 3) * (4 - 2 * (cnt % 2)) * f(__a		)
								cnt += 1
				y += (h / 3.0) * f(__a		)
				return y

def       A_   (						__a  :					Any			,		__a  :					Any			,		__a  :					List[Any]		):

				"""simple docstring"""
				a__					   =		a + h
				while x < (b - h):
								yield x
								a__					   =		x + h

def       A_   (						__a  :					Optional[int]		):  # enter your function here

				"""simple docstring"""
				a__					   =		(x - 0) * (x - 0)
				return y

def       A_   (						):

				"""simple docstring"""
				a__					   =		0.0  # Lower bound of integration
				a__					   =		1.0  # Upper bound of integration
				a__					   =		1_0.0  # define number of steps or resolution
				a__					   =		[a, b]  # define boundary of integration
				a__					   =		method_a(__a			,		__a		)
				print(F'''y = {y}'''		)


if __name__ == "__main__":
	main()






import random







class 				a_    :

						def __init__(       self      :Union[str, Any]  ,		_lowercase      :float  ,		_lowercase      :float)						->   None:
												UpperCAmelCase_					=	x
												UpperCAmelCase_					=	y

						def       __a			(       self      :str)						->   bool:
												return (self.x**2 + self.y**2) <= 1




						@classmethod
						def       __a			(       cls      :Optional[Any])						->   str:
												return cls(x=random.random()  ,		y=random.random())







def 							A     (						__UpperCAmelCase      )			->			float:



						'''simple docstring'''






						if number_of_simulations < 1:
												raise ValueError('''At least one simulation is necessary to estimate PI.'''      )

						UpperCAmelCase_					=	0
						for _ in range(__UpperCAmelCase      ):
												UpperCAmelCase_					=	Point.random_unit_square()

												if random_point.is_in_unit_circle():
																		number_in_unit_circle += 1

						return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
							# import doctest

							# doctest.testmod()
							from math import pi

							UpperCamelCase_      			=  "Please enter the desired number of Monte Carlo simulations: "
							UpperCamelCase_      			=  estimate_pi(int(input(prompt).strip()))
							print(f"An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}")





