


__snake_case   							=						{
    '''a''': '''AAAAA''',
    '''b''': '''AAAAB''',
    '''c''': '''AAABA''',
    '''d''': '''AAABB''',
    '''e''': '''AABAA''',
    '''f''': '''AABAB''',
    '''g''': '''AABBA''',
    '''h''': '''AABBB''',
    '''i''': '''ABAAA''',
    '''j''': '''BBBAA''',
    '''k''': '''ABAAB''',
    '''l''': '''ABABA''',
    '''m''': '''ABABB''',
    '''n''': '''ABBAA''',
    '''o''': '''ABBAB''',
    '''p''': '''ABBBA''',
    '''q''': '''ABBBB''',
    '''r''': '''BAAAA''',
    '''s''': '''BAAAB''',
    '''t''': '''BAABA''',
    '''u''': '''BAABB''',
    '''v''': '''BBBAB''',
    '''w''': '''BABAA''',
    '''x''': '''BABAB''',
    '''y''': '''BABBA''',
    '''z''': '''BABBB''',
    ''' ''': ''' ''',
}


__snake_case   							=						{value: key for key, value in encode_dict.items()}






def 		_A		(		_lowercase )					-> str:


     """simple docstring"""


     __UpperCamelCase =			''
     for letter in word.lower():
          if letter.isalpha() or letter == " ":
               encoded += encode_dict[letter]
          else:
               raise Exception('encode() accepts only letters of the alphabet and spaces' )
     return encoded






def 		_A		(		_lowercase )					-> str:


     """simple docstring"""


     if set(_lowercase ) - {"A", "B", " "} != set():
          raise Exception('decode() accepts only \'A\', \'B\' and spaces' )
     __UpperCamelCase =			''
     for word in coded.split():
          while len(_lowercase ) != 0:
               decoded += decode_dict[word[:5]]
               __UpperCamelCase =			word[5:]
          decoded += " "
     return decoded.strip()


if __name__ == "__main__":
    from doctest import testmod

    testmod()





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



def 			_A	(      SCREAMING_SNAKE_CASE      ):

	# A local function to see if a dot lands in the circle.
	def is_in_circle(SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE      ) -> bool:
		UpperCAmelCase__:	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
	UpperCAmelCase__:	Optional[int]									= 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.
	UpperCAmelCase__:	Optional[int]									= 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	(      SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE = 0.0	,SCREAMING_SNAKE_CASE = 1.0	,):
	return mean(
	    function_to_integrate(uniform(SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE      )      ) for _ in range(SCREAMING_SNAKE_CASE      )      ) * (max_value - min_value)



def 			_A	(      SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE = 0.0	,SCREAMING_SNAKE_CASE = 1.0      ):

	def identity_function(SCREAMING_SNAKE_CASE      ) -> float:
		return x

	UpperCAmelCase__:	Tuple									= area_under_curve_estimator(
	    SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE      )
	UpperCAmelCase__:	Optional[Any]									= (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	(      SCREAMING_SNAKE_CASE      ):

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

	UpperCAmelCase__:	Union[str, Any]									= 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()