
'''simple docstring'''







from __future__ import annotations

import unittest

import numpy as np

from transformers import LayoutLMConfig, is_tf_available
from transformers.testing_utils import require_tf, slow

from ...test_configuration_common import ConfigTester
from ...test_modeling_tf_common import TFModelTesterMixin, ids_tensor, random_attention_mask
from ...test_pipeline_mixin import PipelineTesterMixin


if is_tf_available():
						import tensorflow as tf

						from transformers.models.layoutlm.modeling_tf_layoutlm import (
						    TF_LAYOUTLM_PRETRAINED_MODEL_ARCHIVE_LIST,
						    TFLayoutLMForMaskedLM,
						    TFLayoutLMForQuestionAnswering,
						    TFLayoutLMForSequenceClassification,
						    TFLayoutLMForTokenClassification,
						    TFLayoutLMModel,
						)


class 			lowerCAmelCase :




		def __init__(				self					,						UpperCamelCase					,						UpperCamelCase=13					,						UpperCamelCase=7					,						UpperCamelCase=True					,						UpperCamelCase=True					,						UpperCamelCase=True					,						UpperCamelCase=True					,						UpperCamelCase=99					,						UpperCamelCase=32					,						UpperCamelCase=2					,						UpperCamelCase=4					,						UpperCamelCase=37					,						UpperCamelCase="gelu"					,						UpperCamelCase=0.1					,						UpperCamelCase=0.1					,						UpperCamelCase=512					,						UpperCamelCase=16					,						UpperCamelCase=2					,						UpperCamelCase=0.02					,						UpperCamelCase=3					,						UpperCamelCase=4					,						UpperCamelCase=None					,						UpperCamelCase=1_000					,						):
								_SCREAMING_SNAKE_CASE				= parent
								_SCREAMING_SNAKE_CASE				= batch_size
								_SCREAMING_SNAKE_CASE				= seq_length
								_SCREAMING_SNAKE_CASE				= is_training
								_SCREAMING_SNAKE_CASE				= use_input_mask
								_SCREAMING_SNAKE_CASE				= use_token_type_ids
								_SCREAMING_SNAKE_CASE				= use_labels
								_SCREAMING_SNAKE_CASE				= vocab_size
								_SCREAMING_SNAKE_CASE				= hidden_size
								_SCREAMING_SNAKE_CASE				= num_hidden_layers
								_SCREAMING_SNAKE_CASE				= num_attention_heads
								_SCREAMING_SNAKE_CASE				= intermediate_size
								_SCREAMING_SNAKE_CASE				= hidden_act
								_SCREAMING_SNAKE_CASE				= hidden_dropout_prob
								_SCREAMING_SNAKE_CASE				= attention_probs_dropout_prob
								_SCREAMING_SNAKE_CASE				= max_position_embeddings
								_SCREAMING_SNAKE_CASE				= type_vocab_size
								_SCREAMING_SNAKE_CASE				= type_sequence_label_size
								_SCREAMING_SNAKE_CASE				= initializer_range
								_SCREAMING_SNAKE_CASE				= num_labels
								_SCREAMING_SNAKE_CASE				= num_choices
								_SCREAMING_SNAKE_CASE				= scope
								_SCREAMING_SNAKE_CASE				= range_bbox




		def     lowercase       (				self      ):
								_SCREAMING_SNAKE_CASE				= ids_tensor([self.batch_size, self.seq_length]					,						self.vocab_size      )

								# convert bbox to numpy since TF does not support item assignment
								_SCREAMING_SNAKE_CASE				= ids_tensor([self.batch_size, self.seq_length, 4]					,						self.range_bbox      ).numpy()
								# Ensure that bbox is legal
								for i in range(bbox.shape[0]      ):
														for j in range(bbox.shape[1]      ):
																				if bbox[i, j, 3] < bbox[i, j, 1]:
																										_SCREAMING_SNAKE_CASE				= bbox[i, j, 3]
																										_SCREAMING_SNAKE_CASE				= bbox[i, j, 1]
																										_SCREAMING_SNAKE_CASE				= t
																				if bbox[i, j, 2] < bbox[i, j, 0]:
																										_SCREAMING_SNAKE_CASE				= bbox[i, j, 2]
																										_SCREAMING_SNAKE_CASE				= bbox[i, j, 0]
																										_SCREAMING_SNAKE_CASE				= t
								_SCREAMING_SNAKE_CASE				= tf.convert_to_tensor(UpperCamelCase      )

								_SCREAMING_SNAKE_CASE				= None
								if self.use_input_mask:
														_SCREAMING_SNAKE_CASE				= random_attention_mask([self.batch_size, self.seq_length]      )

								_SCREAMING_SNAKE_CASE				= None
								if self.use_token_type_ids:
														_SCREAMING_SNAKE_CASE				= ids_tensor([self.batch_size, self.seq_length]					,						self.type_vocab_size      )

								_SCREAMING_SNAKE_CASE				= None
								_SCREAMING_SNAKE_CASE				= None
								_SCREAMING_SNAKE_CASE				= None
								if self.use_labels:
														_SCREAMING_SNAKE_CASE				= ids_tensor([self.batch_size]					,						self.type_sequence_label_size      )
														_SCREAMING_SNAKE_CASE				= ids_tensor([self.batch_size, self.seq_length]					,						self.num_labels      )
														_SCREAMING_SNAKE_CASE				= ids_tensor([self.batch_size]					,						self.num_choices      )

								_SCREAMING_SNAKE_CASE				= LayoutLMConfig(
								    vocab_size=self.vocab_size					,						hidden_size=self.hidden_size					,						num_hidden_layers=self.num_hidden_layers					,						num_attention_heads=self.num_attention_heads					,						intermediate_size=self.intermediate_size					,						hidden_act=self.hidden_act					,						hidden_dropout_prob=self.hidden_dropout_prob					,						attention_probs_dropout_prob=self.attention_probs_dropout_prob					,						max_position_embeddings=self.max_position_embeddings					,						type_vocab_size=self.type_vocab_size					,						initializer_range=self.initializer_range					,						)

								return config, input_ids, bbox, token_type_ids, input_mask, sequence_labels, token_labels, choice_labels




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase      ):
								_SCREAMING_SNAKE_CASE				= TFLayoutLMModel(config=UpperCamelCase      )

								_SCREAMING_SNAKE_CASE				= model(UpperCamelCase					,						UpperCamelCase					,						attention_mask=UpperCamelCase					,						token_type_ids=UpperCamelCase      )
								_SCREAMING_SNAKE_CASE				= model(UpperCamelCase					,						UpperCamelCase					,						token_type_ids=UpperCamelCase      )
								_SCREAMING_SNAKE_CASE				= model(UpperCamelCase					,						UpperCamelCase      )
								self.parent.assertEqual(result.last_hidden_state.shape					,						(self.batch_size, self.seq_length, self.hidden_size)      )
								self.parent.assertEqual(result.pooler_output.shape					,						(self.batch_size, self.hidden_size)      )




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase      ):
								_SCREAMING_SNAKE_CASE				= TFLayoutLMForMaskedLM(config=UpperCamelCase      )

								_SCREAMING_SNAKE_CASE				= model(UpperCamelCase					,						UpperCamelCase					,						attention_mask=UpperCamelCase					,						token_type_ids=UpperCamelCase					,						labels=UpperCamelCase      )
								self.parent.assertEqual(result.logits.shape					,						(self.batch_size, self.seq_length, self.vocab_size)      )




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase      ):
								_SCREAMING_SNAKE_CASE				= self.num_labels
								_SCREAMING_SNAKE_CASE				= TFLayoutLMForSequenceClassification(config=UpperCamelCase      )

								_SCREAMING_SNAKE_CASE				= model(UpperCamelCase					,						UpperCamelCase					,						attention_mask=UpperCamelCase					,						token_type_ids=UpperCamelCase      )
								self.parent.assertEqual(result.logits.shape					,						(self.batch_size, self.num_labels)      )




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase      ):
								_SCREAMING_SNAKE_CASE				= self.num_labels
								_SCREAMING_SNAKE_CASE				= TFLayoutLMForTokenClassification(config=UpperCamelCase      )

								_SCREAMING_SNAKE_CASE				= model(UpperCamelCase					,						UpperCamelCase					,						attention_mask=UpperCamelCase					,						token_type_ids=UpperCamelCase					,						labels=UpperCamelCase      )
								self.parent.assertEqual(result.logits.shape					,						(self.batch_size, self.seq_length, self.num_labels)      )




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase      ):
								_SCREAMING_SNAKE_CASE				= TFLayoutLMForQuestionAnswering(config=UpperCamelCase      )

								_SCREAMING_SNAKE_CASE				= model(UpperCamelCase					,						UpperCamelCase					,						attention_mask=UpperCamelCase					,						token_type_ids=UpperCamelCase      )
								self.parent.assertEqual(result.start_logits.shape					,						(self.batch_size, self.seq_length)      )
								self.parent.assertEqual(result.end_logits.shape					,						(self.batch_size, self.seq_length)      )




		def     lowercase       (				self      ):
								_SCREAMING_SNAKE_CASE				= self.prepare_config_and_inputs()
								(
								    (
								    _SCREAMING_SNAKE_CASE
								),							(
								    _SCREAMING_SNAKE_CASE
								),							(
								    _SCREAMING_SNAKE_CASE
								),							(
								    _SCREAMING_SNAKE_CASE
								),							(
								    _SCREAMING_SNAKE_CASE
								),							(
								    _SCREAMING_SNAKE_CASE
								),							(
								    _SCREAMING_SNAKE_CASE
								),							(
								    _SCREAMING_SNAKE_CASE
								),							
								)				= config_and_inputs
								_SCREAMING_SNAKE_CASE				= {
								    "input_ids": input_ids,
								    "bbox": bbox,
								    "token_type_ids": token_type_ids,
								    "attention_mask": input_mask,
								}
								return config, inputs_dict


@require_tf
class 			lowerCAmelCase (				__UpperCAmelCase		,     __UpperCAmelCase		,     unittest.TestCase			):
		a							:					Any       =					(
		    (
		        TFLayoutLMModel,
		        TFLayoutLMForMaskedLM,
		        TFLayoutLMForTokenClassification,
		        TFLayoutLMForSequenceClassification,
		        TFLayoutLMForQuestionAnswering,
		    )
		    if is_tf_available()
		    else ()
		)
		a							:					Union[str, Any]       =					(
		    {
		        """feature-extraction""": TFLayoutLMModel,
		        """fill-mask""": TFLayoutLMForMaskedLM,
		        """text-classification""": TFLayoutLMForSequenceClassification,
		        """token-classification""": TFLayoutLMForTokenClassification,
		        """zero-shot""": TFLayoutLMForSequenceClassification,
		    }
		    if is_tf_available()
		    else {}
		)
		a							:					int       =					False
		a							:					Dict       =					True
		a							:					str       =					10




		def     lowercase       (				self      ):
								_SCREAMING_SNAKE_CASE				= TFLayoutLMModelTester(self      )
								_SCREAMING_SNAKE_CASE				= ConfigTester(self					,						config_class=UpperCamelCase					,						hidden_size=37      )




		def     lowercase       (				self      ):
								self.config_tester.run_common_tests()




		def     lowercase       (				self      ):
								_SCREAMING_SNAKE_CASE				= self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_model(*UpperCamelCase      )




		def     lowercase       (				self      ):
								_SCREAMING_SNAKE_CASE				= self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_for_masked_lm(*UpperCamelCase      )




		def     lowercase       (				self      ):
								_SCREAMING_SNAKE_CASE				= self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_for_sequence_classification(*UpperCamelCase      )




		def     lowercase       (				self      ):
								_SCREAMING_SNAKE_CASE				= self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_for_token_classification(*UpperCamelCase      )




		def     lowercase       (				self      ):
								_SCREAMING_SNAKE_CASE				= self.model_tester.prepare_config_and_inputs()
								self.model_tester.create_and_check_for_question_answering(*UpperCamelCase      )




		@slow
		def     lowercase       (				self      ):
								for model_name in TF_LAYOUTLM_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
														_SCREAMING_SNAKE_CASE				= TFLayoutLMModel.from_pretrained(UpperCamelCase      )
														self.assertIsNotNone(UpperCamelCase      )




		@unittest.skip("Onnx compliancy broke with TF 2.10"      )
		def     lowercase       (				self      ):
								pass



def 			_a		(	):
						# Here we prepare a batch of 2 sequences to test a LayoutLM forward pass on:
						# fmt: off
						_SCREAMING_SNAKE_CASE				= tf.convert_to_tensor([[101,1019,1014,1016,1037,1_2849,4747,1004,1_4246,2278,5439,4524,5002,2930,2193,2930,4341,3208,1005,1055,2171,2848,1_1300,3531,102],[101,4070,4034,7020,1024,3058,1015,1013,2861,1013,6070,1_9274,2772,6205,2_7814,1_6147,1_6147,4343,2047,1_0283,1_0969,1_4389,1012,2338,102]]  )  # noqa: E231
						_SCREAMING_SNAKE_CASE				= tf.convert_to_tensor([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],]  )  # noqa: E231
						_SCREAMING_SNAKE_CASE				= tf.convert_to_tensor([[[0,0,0,0],[423,237,440,251],[427,272,441,287],[419,115,437,129],[961,885,992,912],[256,38,330,58],[256,38,330,58],[336,42,353,57],[360,39,401,56],[360,39,401,56],[411,39,471,59],[479,41,528,59],[533,39,630,60],[67,113,134,131],[141,115,209,132],[68,149,133,166],[141,149,187,164],[195,148,287,165],[195,148,287,165],[195,148,287,165],[295,148,349,165],[441,149,492,166],[497,149,546,164],[64,201,125,218],[1000,1000,1000,1000]],[[0,0,0,0],[662,150,754,166],[665,199,742,211],[519,213,554,228],[519,213,554,228],[134,433,187,454],[130,467,204,480],[130,467,204,480],[130,467,204,480],[130,467,204,480],[130,467,204,480],[314,469,376,482],[504,684,582,706],[941,825,973,900],[941,825,973,900],[941,825,973,900],[941,825,973,900],[610,749,652,765],[130,659,168,672],[176,657,237,672],[238,657,312,672],[443,653,628,672],[443,653,628,672],[716,301,825,317],[1000,1000,1000,1000]]]  )  # noqa: E231
						_SCREAMING_SNAKE_CASE				= tf.convert_to_tensor([[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]  )  # noqa: E231
						# these are sequence labels (i.e. at the token level)
						_SCREAMING_SNAKE_CASE				= tf.convert_to_tensor([[-100,10,10,10,9,1,-100,7,7,-100,7,7,4,2,5,2,8,8,-100,-100,5,0,3,2,-100],[-100,12,12,12,-100,12,10,-100,-100,-100,-100,10,12,9,-100,-100,-100,10,10,10,9,12,-100,10,-100]]  )  # noqa: E231
						# fmt: on

						return input_ids, attention_mask, bbox, token_type_ids, labels




@require_tf
class 			lowerCAmelCase (				unittest.TestCase			):




		@slow
		def     lowercase       (				self      ):
								_SCREAMING_SNAKE_CASE				= TFLayoutLMModel.from_pretrained("microsoft/layoutlm-base-uncased"      )

								_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE				= prepare_layoutlm_batch_inputs()

								# forward pass
								_SCREAMING_SNAKE_CASE				= model(input_ids=UpperCamelCase					,						bbox=UpperCamelCase					,						attention_mask=UpperCamelCase					,						token_type_ids=UpperCamelCase      )

								# test the sequence output on [0, :3, :3]
								_SCREAMING_SNAKE_CASE				= tf.convert_to_tensor(
								    [[0.17_85, -0.19_47, -0.04_25], [-0.32_54, -0.28_07, 0.25_53], [-0.53_91, -0.33_22, 0.33_64]]					,						)

								self.assertTrue(np.allclose(outputs.last_hidden_state[0, :3, :3]					,						UpperCamelCase					,						atol=1e-3      )      )

								# test the pooled output on [1, :3]
								_SCREAMING_SNAKE_CASE				= tf.convert_to_tensor([-0.65_80, -0.02_14, 0.85_52]      )

								self.assertTrue(np.allclose(outputs.pooler_output[1, :3]					,						UpperCamelCase					,						atol=1e-3      )      )




		@slow
		def     lowercase       (				self      ):
								# initialize model with randomly initialized sequence classification head
								_SCREAMING_SNAKE_CASE				= TFLayoutLMForSequenceClassification.from_pretrained("microsoft/layoutlm-base-uncased"					,						num_labels=2      )

								_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE				= prepare_layoutlm_batch_inputs()

								# forward pass
								_SCREAMING_SNAKE_CASE				= model(
								    input_ids=UpperCamelCase					,						bbox=UpperCamelCase					,						attention_mask=UpperCamelCase					,						token_type_ids=UpperCamelCase					,						labels=tf.convert_to_tensor([1, 1]      )					,						)

								# test whether we get a loss as a scalar
								_SCREAMING_SNAKE_CASE				= outputs.loss
								_SCREAMING_SNAKE_CASE				= (2,)
								self.assertEqual(loss.shape					,						UpperCamelCase      )

								# test the shape of the logits
								_SCREAMING_SNAKE_CASE				= outputs.logits
								_SCREAMING_SNAKE_CASE				= (2, 2)
								self.assertEqual(logits.shape					,						UpperCamelCase      )




		@slow
		def     lowercase       (				self      ):
								# initialize model with randomly initialized token classification head
								_SCREAMING_SNAKE_CASE				= TFLayoutLMForTokenClassification.from_pretrained("microsoft/layoutlm-base-uncased"					,						num_labels=13      )

								_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE				= prepare_layoutlm_batch_inputs()

								# forward pass
								_SCREAMING_SNAKE_CASE				= model(
								    input_ids=UpperCamelCase					,						bbox=UpperCamelCase					,						attention_mask=UpperCamelCase					,						token_type_ids=UpperCamelCase					,						labels=UpperCamelCase      )

								# test the shape of the logits
								_SCREAMING_SNAKE_CASE				= outputs.logits
								_SCREAMING_SNAKE_CASE				= tf.convert_to_tensor((2, 25, 13)      )
								self.assertEqual(logits.shape					,						UpperCamelCase      )




		@slow
		def     lowercase       (				self      ):
								# initialize model with randomly initialized token classification head
								_SCREAMING_SNAKE_CASE				= TFLayoutLMForQuestionAnswering.from_pretrained("microsoft/layoutlm-base-uncased"      )

								_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE				= prepare_layoutlm_batch_inputs()

								# forward pass
								_SCREAMING_SNAKE_CASE				= model(input_ids=UpperCamelCase					,						bbox=UpperCamelCase					,						attention_mask=UpperCamelCase					,						token_type_ids=UpperCamelCase      )

								# test the shape of the logits
								_SCREAMING_SNAKE_CASE				= tf.convert_to_tensor((2, 25)      )
								self.assertEqual(outputs.start_logits.shape					,						UpperCamelCase      )
								self.assertEqual(outputs.end_logits.shape					,						UpperCamelCase      )

'''simple docstring'''







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



def 			_a		(	_SCREAMING_SNAKE_CASE		:   int  ):

						# A local function to see if a dot lands in the circle.
						def is_in_circle(_SCREAMING_SNAKE_CASE		:   float	,			_SCREAMING_SNAKE_CASE		:   float  ) -> bool:
												_SCREAMING_SNAKE_CASE				= 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
						_SCREAMING_SNAKE_CASE				= mean(
						    int(is_in_circle(uniform(-1.0	,			1.0  )	,			uniform(-1.0	,			1.0  )  )  )
						    for _ in range(_SCREAMING_SNAKE_CASE  )  )
						# The ratio of the area for circle to square is pi/4.
						_SCREAMING_SNAKE_CASE				= 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 			_a		(	_SCREAMING_SNAKE_CASE		:   int	,			_SCREAMING_SNAKE_CASE		:   Callable[[float], float]	,			_SCREAMING_SNAKE_CASE		:   float = 0.0	,			_SCREAMING_SNAKE_CASE		:   float = 1.0	,			):
						return mean(
						    function_to_integrate(uniform(_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE  )  ) for _ in range(_SCREAMING_SNAKE_CASE  )  ) * (max_value - min_value)



def 			_a		(	_SCREAMING_SNAKE_CASE		:   int	,			_SCREAMING_SNAKE_CASE		:   float = 0.0	,			_SCREAMING_SNAKE_CASE		:   float = 1.0  ):

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

						_SCREAMING_SNAKE_CASE				= area_under_curve_estimator(
						    _SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE  )
						_SCREAMING_SNAKE_CASE				= (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 			_a		(	_SCREAMING_SNAKE_CASE		:   int  ):

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

						_SCREAMING_SNAKE_CASE				= area_under_curve_estimator(
						    _SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			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()