


from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean
def        UpperCamelCase_(				_A   :int  )->		List[Any]:

			# 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        UpperCamelCase_(				_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        UpperCamelCase_(				_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        UpperCamelCase_(				_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_speech_available,
    is_torch_available,
)


__UpperCamelCase    		=       {
    'configuration_trocr': ['TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP', 'TrOCRConfig'],
    'processing_trocr': ['TrOCRProcessor'],
}


try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__UpperCamelCase    		=       [
						    'TROCR_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'TrOCRForCausalLM',
						    'TrOCRPreTrainedModel',
						]


if TYPE_CHECKING:
						from .configuration_trocr import TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP, TrOCRConfig
						from .processing_trocr import TrOCRProcessor

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_trocr import TROCR_PRETRAINED_MODEL_ARCHIVE_LIST, TrOCRForCausalLM, TrOCRPreTrainedModel

else:
						import sys

						__UpperCamelCase    		=       _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)


