
def 	A_ (							snake_case							:   List[str] )      ->    Any:



						'''simple docstring'''

						__UpperCamelCase       =			[]
						__UpperCamelCase       =			[]
						__UpperCamelCase       =			{
						    '''^''': 3,
						    '''*''': 2,
						    '''/''': 2,
						    '''%''': 2,
						    '''+''': 1,
						    '''-''': 1,
						}  # Priority of each operator
						__UpperCamelCase       =			len(snake_case ) if (len(snake_case ) > 7) else 7

						# Print table header for output
						print(
						    '''Symbol'''.center(8 ) ,      '''Stack'''.center(snake_case ) ,      '''Postfix'''.center(snake_case ) ,      sep=''' | ''' ,      )
						print('''-''' * (print_width * 3 + 7) )

						for x in infix:
												if x.isalpha() or x.isdigit():
																		post_fix.append(snake_case )  # if x is Alphabet / Digit, add it to Postfix
												elif x == "(":
																		stack.append(snake_case )  # if x is "(" push to Stack
												elif x == ")":  # if x is ")" pop stack until "(" is encountered
																		while stack[-1] != "(":
																								post_fix.append(stack.pop() )  # Pop stack & add the content to Postfix
																		stack.pop()
												else:
																		if len(snake_case ) == 0:
																								stack.append(snake_case )  # If stack is empty, push x to stack
																		else:  # while priority of x is not > priority of element in the stack
																								while len(snake_case ) > 0 and priority[x] <= priority[stack[-1]]:
																														post_fix.append(stack.pop() )  # pop stack & add to Postfix
																								stack.append(snake_case )  # push x to stack

												print(
												    x.center(8 ) ,      (''''''.join(snake_case )).ljust(snake_case ) ,      (''''''.join(snake_case )).ljust(snake_case ) ,      sep=''' | ''' ,      )  # Output in tabular format

						while len(snake_case ) > 0:  # while stack is not empty
												post_fix.append(stack.pop() )  # pop stack & add to Postfix
												print(
												    ''' '''.center(8 ) ,      (''''''.join(snake_case )).ljust(snake_case ) ,      (''''''.join(snake_case )).ljust(snake_case ) ,      sep=''' | ''' ,      )  # Output in tabular format

						return "".join(snake_case )  # return Postfix as str




def 	A_ (							snake_case							:   str )      ->    Optional[Any]:



						'''simple docstring'''

						__UpperCamelCase       =			list(infix[::-1] )  # reverse the infix equation

						for i in range(len(snake_case ) ):
												if infix[i] == "(":
																		__UpperCamelCase       =			''')'''  # change "(" to ")"
												elif infix[i] == ")":
																		__UpperCamelCase       =			'''('''  # change ")" to "("

						return (infix_2_postfix(''''''.join(snake_case ) ))[
						    ::-1
						]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
					lowercase__							:							Union[str, Any]									=			input("\nEnter an Infix Equation = ")  # Input an Infix equation
					lowercase__							:							Union[str, Any]									=			"".join(Infix.split())  # Remove spaces from the input
					print("\n\t", Infix, "(Infix) -> ", infix_2_prefix(Infix), "(Prefix)")






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




def 	A_ (							snake_case							:   int )      ->    int:



						'''simple docstring'''

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



						'''simple docstring'''

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




def 	A_ (							snake_case							:   int ,      snake_case							:   float = 0.0 ,      snake_case							:   float = 1.0 )      ->    None:



						'''simple docstring'''

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

						__UpperCamelCase       =			area_under_curve_estimator(
						    snake_case ,      snake_case ,      snake_case ,      snake_case )
						__UpperCamelCase       =			(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 	A_ (							snake_case							:   int )      ->    None:



						'''simple docstring'''

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

						__UpperCamelCase       =			area_under_curve_estimator(
						    snake_case ,      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()




