





from __future__ import annotations

from collections.abc import Callable





def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__			,			UpperCamelCase__			,			UpperCamelCase__			,			UpperCamelCase__ = 100			,			)  ->				float:







			'''simple docstring'''

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


if __name__ == "__main__":





				def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__ )  ->				str:







							'''simple docstring'''

							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:")
				__A				:    List[Any]       =   10
				while i <= 100_000:
								print(F'with {i} steps: {trapezoidal_area(f, -5, 5, i)}')
								i *= 10










def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__			,			UpperCamelCase__			,			UpperCamelCase__ )  ->				int:







			'''simple docstring'''

			if exponent == 1:
						return base
			if exponent % 2 == 0:
						UpperCAmelCase   		=				_modexpt(UpperCamelCase__			,			exponent // 2			,			UpperCamelCase__ ) % modulo_value
						return (x * x) % modulo_value
			else:
						return (base * _modexpt(UpperCamelCase__			,			exponent - 1			,			UpperCamelCase__ )) % modulo_value





def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__ = 1777			,			UpperCamelCase__ = 1855			,			UpperCamelCase__ = 8 )  ->				int:







			'''simple docstring'''

			UpperCAmelCase   		=				base
			for _ in range(1			,			UpperCamelCase__ ):
						UpperCAmelCase   		=				_modexpt(UpperCamelCase__			,			UpperCamelCase__			,			10**digits )

			return result


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



