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




def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ):

 # A local function to see if a dot lands in the circle.
 def is_in_circle(lowerCAmelCase__							:    float  ,       lowerCAmelCase__							:    float  ) -> bool:
  __a			:  int		    =  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			:  List[str]		    =  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			:  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        __UpperCamelCase					(    lowerCAmelCase__							:    int  ,       lowerCAmelCase__							:    Callable[[float], float]  ,       lowerCAmelCase__							:    float = 0.0  ,       lowerCAmelCase__							:    float = 1.0  ,       ):
 return mean(
     function_to_integrate(uniform(lowerCAmelCase__  ,       lowerCAmelCase__  )  ) for _ in range(lowerCAmelCase__  )  ) * (max_value - min_value)




def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ,       lowerCAmelCase__							:    float = 0.0  ,       lowerCAmelCase__							:    float = 1.0  ):

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

 __a			:  List[str]		    =  area_under_curve_estimator(
     lowerCAmelCase__  ,       lowerCAmelCase__  ,       lowerCAmelCase__  ,       lowerCAmelCase__  )
 __a			:  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        __UpperCamelCase					(    lowerCAmelCase__							:    int  ):

 def function_to_integrate(lowerCAmelCase__							:    float  ) -> 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()


from .glue import GlueDataset, GlueDataTrainingArguments
from .language_modeling import (
    LineByLineTextDataset,
    LineByLineWithRefDataset,
    LineByLineWithSOPTextDataset,
    TextDataset,
    TextDatasetForNextSentencePrediction,
)
from .squad import SquadDataset, SquadDataTrainingArguments
