
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     : Tuple				,					__lowerCamelCase     : int    ) -> bool:
              snake_case       :   Union[str, 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
       snake_case       :   Optional[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.
       snake_case       :   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 			UpperCamelCase					(    __lowerCamelCase     : Union[str, Any]				,					__lowerCamelCase     : Optional[int]				,					__lowerCamelCase     : Tuple = 0.0				,					__lowerCamelCase     : Dict = 1.0				,					):
       return mean(
           function_to_integrate(uniform(__lowerCamelCase				,					__lowerCamelCase    )    ) for _ in range(__lowerCamelCase    )    ) * (max_value - min_value)


def 			UpperCamelCase					(    __lowerCamelCase     : str				,					__lowerCamelCase     : Any = 0.0				,					__lowerCamelCase     : List[str] = 1.0    ):

       def identity_function(__lowerCamelCase     : Optional[Any]    ) -> float:
              return x

       snake_case       :   List[Any]							=      area_under_curve_estimator(
           __lowerCamelCase				,					__lowerCamelCase				,					__lowerCamelCase				,					__lowerCamelCase    )
       snake_case       :   Dict							=      (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     : List[str]    ):

       def function_to_integrate(__lowerCamelCase     : List[Any]    ) -> float:
              return sqrt(4.0 - x * x    )

       snake_case       :   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()










"""simple docstring"""







from dataclasses import dataclass, field
from typing import TYPE_CHECKING, Any, ClassVar, Dict, List, Optional, Union

import pyarrow as pa


if TYPE_CHECKING:
							from .features import FeatureType
@dataclass
class        __A       :







		'''simple docstring'''





		lowerCAmelCase			:					List[str]
		lowerCAmelCase			:					Optional[str]   	=				None
		# Automatically constructed
		lowerCAmelCase			:					ClassVar[str]   	=				"dict"
		lowerCAmelCase			:					ClassVar[Any]   	=				None
		lowerCAmelCase			:					str   	=				field(default="Translation"     ,init=A_     ,repr=A_    )







		def __call__(	self						:  List[str]						)					->		Any:






				"""simple docstring"""



				return pa.struct({lang: pa.string() for lang in sorted(self.languages						)}						)







		def 					UpperCAmelCase    (	self						:  List[str]						)					->		Union["FeatureType", Dict[str, "FeatureType"]]:






				"""simple docstring"""



				from .features import Value

				return {k: Value('''string'''						) for k in sorted(self.languages						)}





@dataclass
class        __A       :







		'''simple docstring'''





		lowerCAmelCase			:					Optional[List]   	=				None
		lowerCAmelCase			:					Optional[int]   	=				None
		lowerCAmelCase			:					Optional[str]   	=				None
		# Automatically constructed
		lowerCAmelCase			:					ClassVar[str]   	=				"dict"
		lowerCAmelCase			:					ClassVar[Any]   	=				None
		lowerCAmelCase			:					str   	=				field(default="TranslationVariableLanguages"     ,init=A_     ,repr=A_    )







		def 					UpperCAmelCase    (	self						:  List[Any]						)					->		Optional[int]:






				"""simple docstring"""



				lowercase__   :    Optional[int]				=			sorted(set(self.languages						)						) if self.languages else None
				lowercase__   :    Dict				=			len(self.languages						) if self.languages else None







		def __call__(	self						:  List[Any]						)					->		List[Any]:






				"""simple docstring"""



				return pa.struct({'''language''': pa.list_(pa.string()						), '''translation''': pa.list_(pa.string()						)}						)







		def 					UpperCAmelCase    (	self						:  Dict			,_snake_case						:  Tuple						)					->		int:






				"""simple docstring"""



				lowercase__   :    List[Any]				=			set(self.languages						)
				if self.languages and set(_snake_case						) - lang_set:
						raise ValueError(
						    f"""Some languages in example ({", ".join(sorted(set(_snake_case						) - lang_set						)						)}) are not in valid set ({", ".join(_snake_case						)})."""						)

				# Convert dictionary into tuples, splitting out cases where there are
				# multiple translations for a single language.
				lowercase__   :    str				=			[]
				for lang, text in translation_dict.items():
						if isinstance(_snake_case			,_snake_case						):
								translation_tuples.append((lang, text)						)
						else:
								translation_tuples.extend([(lang, el) for el in text]						)

        # Ensure translations are in ascending order by language code.
				lowercase__		,			lowercase__   :    Optional[Any]				=			zip(*sorted(_snake_case						)						)

				return {"language": languages, "translation": translations}







		def 					UpperCAmelCase    (	self						:  List[Any]						)					->		Union["FeatureType", Dict[str, "FeatureType"]]:






				"""simple docstring"""



				from .features import Sequence, Value

				return {
				    "language": Sequence(Value('''string'''						)						),
				    "translation": Sequence(Value('''string'''						)						),
				}
