

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






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					List[str]:

	# A local function to see if a dot lands in the circle.
	def is_in_circle(lowerCamelCase__     ,			lowerCamelCase__      ) -> bool:
		__lowerCamelCase    :    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
	__lowerCamelCase    :    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.
	__lowerCamelCase    :    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        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__ = 0.0     ,			lowerCamelCase__ = 1.0     ,			)  ->					Tuple:
	return mean(
	    function_to_integrate(uniform(lowerCAmelCase__     ,			lowerCAmelCase__      )      ) for _ in range(lowerCAmelCase__      )      ) * (max_value - min_value)






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__ = 0.0     ,			lowerCamelCase__ = 1.0      )  ->					Dict:

	def identity_function(lowerCamelCase__      ) -> float:
		return x

	__lowerCamelCase    :    List[str] 	=			area_under_curve_estimator(
	    lowerCAmelCase__     ,			lowerCAmelCase__     ,			lowerCAmelCase__     ,			lowerCAmelCase__      )
	__lowerCamelCase    :    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        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					Tuple:

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

	__lowerCamelCase    :    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 typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


a		={
    """configuration_bigbird_pegasus""": [
        """BIGBIRD_PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """BigBirdPegasusConfig""",
        """BigBirdPegasusOnnxConfig""",
    ],
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					a		=[
					    """BIGBIRD_PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """BigBirdPegasusForCausalLM""",
					    """BigBirdPegasusForConditionalGeneration""",
					    """BigBirdPegasusForQuestionAnswering""",
					    """BigBirdPegasusForSequenceClassification""",
					    """BigBirdPegasusModel""",
					    """BigBirdPegasusPreTrainedModel""",
					]


if TYPE_CHECKING:
					from .configuration_bigbird_pegasus import (
					    BIGBIRD_PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP,
					    BigBirdPegasusConfig,
					    BigBirdPegasusOnnxConfig,
					)

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_bigbird_pegasus import (
										    BIGBIRD_PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST,
										    BigBirdPegasusForCausalLM,
										    BigBirdPegasusForConditionalGeneration,
										    BigBirdPegasusForQuestionAnswering,
										    BigBirdPegasusForSequenceClassification,
										    BigBirdPegasusModel,
										    BigBirdPegasusPreTrainedModel,
										)


else:
					import sys

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




