


def 							__lowercase       (			__lowerCAmelCase							:    int ,   __lowerCAmelCase							:    Tuple       ):
							a__					=					(boundary[1] - boundary[0]) / steps
							a__					=					boundary[0]
							a__					=					boundary[1]
							a__					=					make_points(UpperCamelCase__ ,   UpperCamelCase__ ,   UpperCamelCase__       )
							a__					=					0.0
							y += (h / 2.0) * f(UpperCamelCase__       )
							for i in x_i:
														# print(i)
														y += h * f(UpperCamelCase__       )
							y += (h / 2.0) * f(UpperCamelCase__       )
							return y






def 							__lowercase       (			__lowerCAmelCase							:    Union[str, Any] ,   __lowerCAmelCase							:    List[str] ,   __lowerCAmelCase							:    Optional[Any]       ):
							a__					=					a + h
							while x < (b - h):
														yield x
														a__					=					x + h






def 							__lowercase       (			__lowerCAmelCase							:    int       ):  # enter your function here
							a__					=					(x - 0) * (x - 0)
							return y






def 							__lowercase       (			):
							a__					=					0.0  # Lower bound of integration
							a__					=					1.0  # Upper bound of integration
							a__					=					10.0  # define number of steps or resolution
							a__					=					[a, b]  # define boundary of integration
							a__					=					method_a(UpperCamelCase__ ,   UpperCamelCase__       )
							print(F'y = {y}'       )


if __name__ == "__main__":
						main()








from math import ceil, sqrt






def 							__lowercase       (			__lowerCAmelCase							:    int = 1_0_0_0_0_0_0       ):
							a__					=					0

							for outer_width in range(3 ,   (limit // 4) + 2       ):
														if outer_width**2 > limit:
																					a__					=					max(ceil(sqrt(outer_width**2 - limit       )       ) ,   1       )
														else:
																					a__					=					1
														if (outer_width - hole_width_lower_bound) % 2:
																					hole_width_lower_bound += 1

														answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

							return answer


if __name__ == "__main__":
						print(f"""{solution() = }""")




