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




def       __lowerCAmelCase      (						A_   : int					)    ->  str:

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




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

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

  __UpperCAmelCase						    =       area_under_curve_estimator(
      A_						,	A_						,	A_						,	A_					)
  __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       __lowerCAmelCase      (						A_   : int					)    ->  None:

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

  __UpperCAmelCase						    =       area_under_curve_estimator(
      A_						,	A_						,	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 typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
    is_vision_available,
)


a_							=      {"""processing_layoutxlm""": ["""LayoutXLMProcessor"""]}

try:
       if not is_sentencepiece_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       a_							=      ["""LayoutXLMTokenizer"""]

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       a_							=      ["""LayoutXLMTokenizerFast"""]

if TYPE_CHECKING:
       from .processing_layoutxlm import LayoutXLMProcessor

       try:
              if not is_sentencepiece_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_layoutxlm import LayoutXLMTokenizer

       try:
              if not is_tokenizers_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_layoutxlm_fast import LayoutXLMTokenizerFast

else:
       import sys

       a_							=      _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



