


"""simple docstring"""



def     __lowerCAmelCase		(		lowercase    :    str		,				lowercase    :    Optional[int]					)      ->		Any:


    """simple docstring"""





    snake_case       : Tuple    =       (boundary[1] - boundary[0]) / steps
    snake_case       : Dict    =       boundary[0]
    snake_case       : Any    =       boundary[1]
    snake_case       : Union[str, Any]    =       make_points(a_		,				a_		,				a_					)
    snake_case       : Any    =       0.0
    y += (h / 2.0) * f(a_					)
    for i in x_i:
        # print(i)
        y += h * f(a_					)
    y += (h / 2.0) * f(a_					)
    return y







def     __lowerCAmelCase		(		lowercase    :    Tuple		,				lowercase    :    Any		,				lowercase    :    Tuple					)      ->		Tuple:


    """simple docstring"""





    snake_case       : Optional[int]    =       a + h
    while x < (b - h):
        yield x
        snake_case       : List[str]    =       x + h







def     __lowerCAmelCase		(		lowercase    :    List[str]					)      ->		Tuple:  # enter your function here


    """simple docstring"""





    snake_case       : int    =       (x - 0) * (x - 0)
    return y







def     __lowerCAmelCase		(		)      ->		Dict:


    """simple docstring"""





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


if __name__ == "__main__":
  main()













'''simple docstring'''

def 				snake_case       (  a_				:			list[int]     , a_				:			list[int]						)							->					tuple[float, float]:





      """simple docstring"""

      if not len(a_						) == len(a_						) == 3:
            raise ValueError("""Please enter a valid equation."""						)
      if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
            raise ValueError("""Both a & b of two equations can't be zero."""						)

      # Extract the coefficients
      UpperCamelCase_     ,      UpperCamelCase_     ,      UpperCamelCase_					: Optional[int]            =				equationa
      UpperCamelCase_     ,      UpperCamelCase_     ,      UpperCamelCase_					: List[str]            =				equationa

      # Calculate the determinants of the matrices
      UpperCamelCase_					: Union[str, Any]            =				aa * ba - aa * ba
      UpperCamelCase_					: Dict            =				ca * ba - ca * ba
      UpperCamelCase_					: Dict            =				aa * ca - aa * ca

      # Check if the system of linear equations has a solution (using Cramer's rule)
      if determinant == 0:
            if determinant_x == determinant_y == 0:
                  raise ValueError("""Infinite solutions. (Consistent system)"""						)
            else:
                  raise ValueError("""No solution. (Inconsistent system)"""						)
      else:
            if determinant_x == determinant_y == 0:
                  # Trivial solution (Inconsistent system)
                  return (0.0, 0.0)
            else:
                  UpperCamelCase_					: List[Any]            =				determinant_x / determinant
                  UpperCamelCase_					: List[str]            =				determinant_y / determinant
                  # Non-Trivial Solution (Consistent system)
                  return (x, y)






