





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




def  lowerCAmelCase_ (							UpperCamelCase_  )     ->		Tuple:



       def is_in_circle(UpperCamelCase_					,		UpperCamelCase_  ) -> 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(_SCREAMING_SNAKE_CASE  )  )
       # 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  lowerCAmelCase_ (							UpperCamelCase_					,		UpperCamelCase_					,		UpperCamelCase_ = 0.0					,		UpperCamelCase_ = 1.0					,		)     ->		Union[str, Any]:
       return mean(
           function_to_integrate(uniform(_SCREAMING_SNAKE_CASE					,		_SCREAMING_SNAKE_CASE  )  ) for _ in range(_SCREAMING_SNAKE_CASE  )  ) * (max_value - min_value)




def  lowerCAmelCase_ (							UpperCamelCase_					,		UpperCamelCase_ = 0.0					,		UpperCamelCase_ = 1.0  )     ->		Optional[int]:



       def identity_function(UpperCamelCase_  ) -> float:
              return x

       UpperCamelCase_          =  area_under_curve_estimator(
           _SCREAMING_SNAKE_CASE					,		_SCREAMING_SNAKE_CASE					,		_SCREAMING_SNAKE_CASE					,		_SCREAMING_SNAKE_CASE  )
       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  lowerCAmelCase_ (							UpperCamelCase_  )     ->		Any:



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

       UpperCamelCase_          =  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()










import unittest

from transformers.testing_utils import CaptureStdout
from transformers.tools.python_interpreter import evaluate




def  lowerCAmelCase_ (							UpperCamelCase_  )     ->		Optional[int]:
       return x + 2







class 							_UpperCamelCase					(	unittest.TestCase     ):

       def lowercase (		self: Optional[int]		)       -> str:




              """simple docstring"""


              UpperCamelCase_          =  "x = 3"
              UpperCamelCase_          =  {}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {}					,   state=_SCREAMING_SNAKE_CASE		)
              assert result == 3
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3}		)

              UpperCamelCase_          =  "x = y"
              UpperCamelCase_          =  {"y": 5}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {}					,   state=_SCREAMING_SNAKE_CASE		)
              # evaluate returns the value of the last assignment.
              assert result == 5
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 5, "y": 5}		)

       def lowercase (		self: List[str]		)       -> Dict:




              """simple docstring"""


              UpperCamelCase_          =  "y = add_two(x)"
              UpperCamelCase_          =  {"x": 3}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {"add_two": add_two}					,   state=_SCREAMING_SNAKE_CASE		)
              assert result == 5
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3, "y": 5}		)

              # Won't work without the tool
              with CaptureStdout() as out:
                     UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {}					,   state=_SCREAMING_SNAKE_CASE		)
              assert result is None
              assert "tried to execute add_two" in out.out

       def lowercase (		self: Union[str, Any]		)       -> str:




              """simple docstring"""


              UpperCamelCase_          =  "x = 3"
              UpperCamelCase_          =  {}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {}					,   state=_SCREAMING_SNAKE_CASE		)
              assert result == 3
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3}		)

       def lowercase (		self: Dict		)       -> Any:




              """simple docstring"""


              UpperCamelCase_          =  "test_dict = {'x': x, 'y': add_two(x)}"
              UpperCamelCase_          =  {"x": 3}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {"add_two": add_two}					,   state=_SCREAMING_SNAKE_CASE		)
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3, "y": 5}		)
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3, "test_dict": {"x": 3, "y": 5}}		)

       def lowercase (		self: List[str]		)       -> Union[str, Any]:




              """simple docstring"""


              UpperCamelCase_          =  "x = 3\ny = 5"
              UpperCamelCase_          =  {}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {}					,   state=_SCREAMING_SNAKE_CASE		)
              # evaluate returns the value of the last assignment.
              assert result == 5
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3, "y": 5}		)

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




              """simple docstring"""


              UpperCamelCase_          =  "text = f'This is x: {x}.'"
              UpperCamelCase_          =  {"x": 3}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {}					,   state=_SCREAMING_SNAKE_CASE		)
              # evaluate returns the value of the last assignment.
              assert result == "This is x: 3."
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3, "text": "This is x: 3."}		)

       def lowercase (		self: int		)       -> Union[str, Any]:




              """simple docstring"""


              UpperCamelCase_          =  "if x <= 3:\n    y = 2\nelse:\n    y = 5"
              UpperCamelCase_          =  {"x": 3}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {}					,   state=_SCREAMING_SNAKE_CASE		)
              # evaluate returns the value of the last assignment.
              assert result == 2
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3, "y": 2}		)

              UpperCamelCase_          =  {"x": 8}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {}					,   state=_SCREAMING_SNAKE_CASE		)
              # evaluate returns the value of the last assignment.
              assert result == 5
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 8, "y": 5}		)

       def lowercase (		self: str		)       -> Optional[Any]:




              """simple docstring"""


              UpperCamelCase_          =  "test_list = [x, add_two(x)]"
              UpperCamelCase_          =  {"x": 3}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {"add_two": add_two}					,   state=_SCREAMING_SNAKE_CASE		)
              self.assertListEqual(_SCREAMING_SNAKE_CASE					,   [3, 5]		)
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3, "test_list": [3, 5]}		)

       def lowercase (		self: List[str]		)       -> int:




              """simple docstring"""


              UpperCamelCase_          =  "y = x"
              UpperCamelCase_          =  {"x": 3}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {}					,   state=_SCREAMING_SNAKE_CASE		)
              assert result == 3
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3, "y": 3}		)

       def lowercase (		self: str		)       -> int:




              """simple docstring"""


              UpperCamelCase_          =  "test_list = [x, add_two(x)]\ntest_list[1]"
              UpperCamelCase_          =  {"x": 3}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {"add_two": add_two}					,   state=_SCREAMING_SNAKE_CASE		)
              assert result == 5
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3, "test_list": [3, 5]}		)

              UpperCamelCase_          =  "test_dict = {'x': x, 'y': add_two(x)}\ntest_dict['y']"
              UpperCamelCase_          =  {"x": 3}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {"add_two": add_two}					,   state=_SCREAMING_SNAKE_CASE		)
              assert result == 5
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 3, "test_dict": {"x": 3, "y": 5}}		)



       def lowercase (		self: Dict		)       -> Optional[int]:




              """simple docstring"""


              UpperCamelCase_          =  "x = 0\nfor i in range(3):\n    x = i"
              UpperCamelCase_          =  {}
              UpperCamelCase_          =  evaluate(_SCREAMING_SNAKE_CASE					,   {"range": range}					,   state=_SCREAMING_SNAKE_CASE		)
              assert result == 2
              self.assertDictEqual(_SCREAMING_SNAKE_CASE					,   {"x": 2, "i": 2}		)

