




"""simple docstring"""





def        _UpperCamelCase     (      UpperCamelCase					,							UpperCamelCase				)      ->      str:


			"""simple docstring"""
			if not isinstance(UpperCamelCase					,							UpperCamelCase				):
						raise ValueError("iterations must be defined as integers"				)
			if not isinstance(UpperCamelCase					,							UpperCamelCase				) or not number >= 1:
						raise ValueError(
						    "starting number must be\n                         and integer and be more than 0"				)
			if not iterations >= 1:
						raise ValueError("Iterations must be done more than 0 times to play FizzBuzz"				)

			__UpperCAmelCase						:			Tuple												=       ""
			while number <= iterations:
						if number % 3 == 0:
									out += "Fizz"
						if number % 5 == 0:
									out += "Buzz"
						if 0 not in (number % 3, number % 5):
									out += str(UpperCamelCase				)

						# print(out)
						number += 1
						out += " "
			return out


if __name__ == "__main__":
					import doctest

					doctest.testmod()




"""simple docstring"""




from __future__ import annotations

from collections.abc import Callable



def 							_lowerCamelCase			(			__a,				__a,				__a,				__a = 100,				):
		SCREAMING_SNAKE_CASE_    			=			x_start
		SCREAMING_SNAKE_CASE_    			=			fnc(__a     )
		SCREAMING_SNAKE_CASE_    			=			0.0
		for _ in range(__a     ):
				# Approximates small segments of curve as linear and solve
				# for trapezoidal area
				SCREAMING_SNAKE_CASE_    			=			(x_end - x_start) / steps + xa
				SCREAMING_SNAKE_CASE_    			=			fnc(__a     )
				area += abs(fxa + fxa     ) * (xa - xa) / 2
				# Increment step
				SCREAMING_SNAKE_CASE_    			=			xa
				SCREAMING_SNAKE_CASE_    			=			fxa
		return area


if __name__ == "__main__":



						def 							_lowerCamelCase			(			__a     ):
								return x**3 + x**2

						print('f(x) = x^3 + x^2')
						print('The area between the curve, x = -5, x = 5 and the x axis is:')
						lowerCAmelCase__				=					10
						while i <= 100000:
												print(f'''with {i} steps: {trapezoidal_area(f, -5, 5, i)}''')
												i *= 10