






'''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)














'''simple docstring'''

def 				snake_case       (  a_				:			str     , a_				:			Optional[int]						)							->					Any:





      """simple docstring"""

      UpperCamelCase_					: Tuple            =				(boundary[1] - boundary[0]) / steps
      UpperCamelCase_					: Dict            =				boundary[0]
      UpperCamelCase_					: Any            =				boundary[1]
      UpperCamelCase_					: Union[str, Any]            =				make_points(a_     , a_     , a_						)
      UpperCamelCase_					: 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 				snake_case       (  a_				:			Tuple     , a_				:			Any     , a_				:			Tuple						)							->					Tuple:





      """simple docstring"""

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



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





      """simple docstring"""

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



def 				snake_case       (  )							->					Dict:





      """simple docstring"""

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


if __name__ == "__main__":
      main()






