




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







def        lowerCAmelCase_			(  snake_case_  ):

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







def        lowerCAmelCase_			(  snake_case_,snake_case_ = 0.0,snake_case_ = 1.0  ):

      def identity_function(snake_case_  ) -> float:
            return x

      _A							:  Any    =		area_under_curve_estimator(
          snake_case_,snake_case_,snake_case_,snake_case_  )
      _A							:  Tuple    =		(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_			(  snake_case_  ):

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

      _A							:  Optional[int]    =		area_under_curve_estimator(
          snake_case_,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()










from unittest import TestCase

from datasets import Sequence, Value
from datasets.arrow_dataset import Dataset







class 		lowercase							(     UpperCamelCase__	):

     def       a__			(						self       )		->							Optional[int]:
           return [
               {"col_1": 3, "col_2": "a"},
               {"col_1": 2, "col_2": "b"},
               {"col_1": 1, "col_2": "c"},
               {"col_1": 0, "col_2": "d"},
           ]

     def       a__			(						self       )		->							Optional[int]:
           _A							:  Union[str, Any]    =		{"""col_1""": [3, 2, 1, 0], """col_2""": ["""a""", """b""", """c""", """d"""]}
           return Dataset.from_dict(_a       )

     def       a__			(						self       )		->							Any:
           _A							:  str    =		self._create_example_records()
           _A							:  List[Any]    =		Dataset.from_list(_a       )
           self.assertListEqual(dset.column_names	,  ["""col_1""", """col_2"""]       )
           for i, r in enumerate(_a       ):
                 self.assertDictEqual(_a	,  example_records[i]       )

     def       a__			(						self       )		->							List[str]:
           _A							:  Dict    =		self._create_example_records()
           _A							:  List[str]    =		Dataset.from_list(_a       )
           _A							:  str    =		Dataset.from_dict({k: [r[k] for r in example_records] for k in example_records[0]}       )
           self.assertEqual(dset.info	,  dset_from_dict.info       )

     def       a__			(						self       )		->							str:  # checks what happens with missing columns
           _A							:  List[str]    =		[{"""col_1""": 1}, {"""col_2""": """x"""}]
           _A							:  List[str]    =		Dataset.from_list(_a       )
           self.assertDictEqual(dset[0]	,  {"""col_1""": 1}       )
           self.assertDictEqual(dset[1]	,  {"""col_1""": None}       )  # NB: first record is used for columns

     def       a__			(						self       )		->							Dict:  # checks if the type can be inferred from the second record
           _A							:  List[Any]    =		[{"""col_1""": []}, {"""col_1""": [1, 2]}]
           _A							:  str    =		Dataset.from_list(_a       )
           self.assertEqual(dset.info.features["""col_1"""]	,  Sequence(Value("""int64"""       )       )       )



     def       a__			(						self       )		->							Dict:
           _A							:  List[str]    =		Dataset.from_list([]       )
           self.assertEqual(len(_a       )	,  0       )
           self.assertListEqual(dset.column_names	,  []       )

