


'''simple docstring'''


def      lowerCamelCase					(      lowerCamelCase  :      Dict							,						lowerCamelCase  :      Union[str, Any]):
      # "extended trapezoidal rule"
      # int(f) = dx/2 * (f1 + 2f2 + ... + fn)
      A_						:  List[Any]          =				(boundary[1] - boundary[0]) / steps
      A_						:  Optional[Any]          =				boundary[0]
      A_						:  List[Any]          =				boundary[1]
      A_						:  Optional[int]          =				make_points(lowerCamelCase							,						lowerCamelCase							,						lowerCamelCase)
      A_						:  Union[str, Any]          =				0.0
      y += (h / 2.0) * f(lowerCamelCase)
      for i in x_i:
            # print(i)
            y += h * f(lowerCamelCase)
      y += (h / 2.0) * f(lowerCamelCase)
      return y




def      lowerCamelCase					(      lowerCamelCase  :      Union[str, Any]							,						lowerCamelCase  :      Union[str, Any]							,						lowerCamelCase  :      Dict):
      A_						:  List[Any]          =				a + h
      while x < (b - h):
            yield x
            A_						:  str          =				x + h




def      lowerCamelCase					(      lowerCamelCase  :      Union[str, Any]):  # enter your function here
      A_						:  Tuple          =				(x - 0) * (x - 0)
      return y




def      lowerCamelCase					(      ):
      A_						:  int          =				0.0  # Lower bound of integration
      A_						:  Optional[Any]          =				1.0  # Upper bound of integration
      A_						:  Optional[Any]          =				10.0  # define number of steps or resolution
      A_						:  Optional[Any]          =				[a, b]  # define boundary of integration
      A_						:  Tuple          =				method_a(lowerCamelCase							,						lowerCamelCase)
      print(F'y = {y}')


if __name__ == "__main__":
  main()




'''simple docstring'''


from ..utils import DummyObject, requires_backends



class 	__lowerCAmelCase		(							metaclass=__SCREAMING_SNAKE_CASE    ):


  '''simple docstring'''







  a_  					=							["""torch""", """torchsde"""]






  def __init__(							self :       Any	,*_a :       Union[str, Any]	,**_a :       Optional[int] ):

        '''simple docstring'''




        requires_backends(self	,["""torch""", """torchsde"""] )






  @classmethod
  def        _a							(							cls :       Optional[int]	,*_a :       List[Any]	,**_a :       Any ):

        '''simple docstring'''




        requires_backends(cls	,["""torch""", """torchsde"""] )






  @classmethod
  def        _a							(							cls :       List[Any]	,*_a :       Tuple	,**_a :       Union[str, Any] ):

        '''simple docstring'''




        requires_backends(cls	,["""torch""", """torchsde"""] )
