




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

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> int:
       lowerCamelCase   :      int			 =					a + h
       while x < (b - h):
              yield x
              lowerCamelCase   :      List[str]			 =					x + h

def      A      (      _SCREAMING_SNAKE_CASE    )	-> Optional[Any]:  # enter your function here
       lowerCamelCase   :      str			 =					(x - 0) * (x - 0)
       return y

def      A      (      )	-> int:
       lowerCamelCase   :      int			 =					0.0  # Lower bound of integration
       lowerCamelCase   :      int			 =					1.0  # Upper bound of integration
       lowerCamelCase   :      Dict			 =					10.0  # define number of steps or resolution
       lowerCamelCase   :      int			 =					[a, b]  # define boundary of integration
       lowerCamelCase   :      str			 =					method_a(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )
       print(f'''y = {y}'''    )


if __name__ == "__main__":
       main()










"""simple docstring"""






from collections.abc import Callable
def      lowerCamelCase       (     _UpperCamelCase		:      Callable[[float], float]       ,			_UpperCamelCase		:      float       ,			_UpperCamelCase		:      float							)		->       float:

							'''simple docstring'''



							__UpperCAmelCase   :						float      							=					a
							__UpperCAmelCase   :						float      							=					b
							if function(_UpperCamelCase							) == 0:  # one of the a or b is a root for the function
														return a
							elif function(_UpperCamelCase							) == 0:
														return b
							elif (
							    function(_UpperCamelCase							) * function(_UpperCamelCase							) > 0
							):  # if none of these are root and they are both positive or negative,
														# then this algorithm can't find the root
														raise ValueError("""could not find root in given interval."""							)
							else:
														__UpperCAmelCase   :						float      							=					start + (end - start) / 2.0
														while abs(start - mid							) > 1_0**-7:  # until precisely equals to 10^-7
																					if function(_UpperCamelCase							) == 0:
																												return mid
																					elif function(_UpperCamelCase							) * function(_UpperCamelCase							) < 0:
																												__UpperCAmelCase   :						Union[str, Any]      							=					mid
																					else:
																												__UpperCAmelCase   :						List[Any]      							=					mid
																					__UpperCAmelCase   :						Optional[Any]      							=					start + (end - start) / 2.0
														return mid
def      lowerCamelCase       (     _UpperCamelCase		:      float							)		->       float:

							'''simple docstring'''



							return x**3 - 2 * x - 5


if __name__ == "__main__":
							print(bisection(f, 1, 1000))

							import doctest

							doctest.testmod()
