





SCREAMING_SNAKE_CASE__       :			str			      =						"""
# Installazione di Transformers
! pip install transformers datasets
# Per installare dalla fonte invece dell'ultima versione rilasciata, commenta il comando sopra e
# rimuovi la modalità commento al comando seguente.
# ! pip install git+https://github.com/huggingface/transformers.git
"""

SCREAMING_SNAKE_CASE__       :			str			      =						[{"""type""": """code""", """content""": INSTALL_CONTENT}]
SCREAMING_SNAKE_CASE__       :			Optional[Any]			      =						{
    """{processor_class}""": """FakeProcessorClass""",
    """{model_class}""": """FakeModelClass""",
    """{object_class}""": """FakeObjectClass""",
}








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






def       _A  (      lowerCamelCase   ):

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






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

   def identity_function(lowerCamelCase   ) -> float:
      return x

   a__	:						int      		=  area_under_curve_estimator(
       lowerCamelCase							, lowerCamelCase							, lowerCamelCase							, lowerCamelCase   )
   a__	:						int      		=  (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  (      lowerCamelCase   ):

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

   a__	:						int      		=  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()

