






def _lowerCAmelCase	(  __lowerCamelCase:Optional[Any] ,						__lowerCamelCase:List[str]   ):

						'''simple docstring'''






						__magic_name__            =     (boundary[1] - boundary[0]) / steps
						__magic_name__            =     boundary[0]
						__magic_name__            =     boundary[1]
						__magic_name__            =     make_points(lowerCamelCase__ ,						lowerCamelCase__ ,						lowerCamelCase__   )
						__magic_name__            =     0.0
						y += (h / 2.0) * f(lowerCamelCase__   )
						for i in x_i:
												# print(i)
												y += h * f(lowerCamelCase__   )
						y += (h / 2.0) * f(lowerCamelCase__   )
						return y






def _lowerCAmelCase	(  __lowerCamelCase:int ,						__lowerCamelCase:Optional[int] ,						__lowerCamelCase:Optional[Any]   ):

						'''simple docstring'''






						__magic_name__            =     a + h
						while x < (b - h):
												yield x
												__magic_name__            =     x + h






def _lowerCAmelCase	(  __lowerCamelCase:Tuple   ):  # enter your function here

						'''simple docstring'''






						__magic_name__            =     (x - 0) * (x - 0)
						return y






def _lowerCAmelCase	(  ):

						'''simple docstring'''






						__magic_name__            =     0.0  # Lower bound of integration
						__magic_name__            =     1.0  # Upper bound of integration
						__magic_name__            =     1_0.0  # define number of steps or resolution
						__magic_name__            =     [a, b]  # define boundary of integration
						__magic_name__            =     method_a(lowerCamelCase__ ,						lowerCamelCase__   )
						print(f'''y = {y}'''   )


if __name__ == "__main__":
			main()











"""simple docstring"""

import colorsys

from PIL import Image  # type: ignore






def _lowerCAmelCase	(  __lowerCamelCase:float ,						__lowerCamelCase:float ,						__lowerCamelCase:int   ):

						'''simple docstring'''






						__magic_name__            =     x
						__magic_name__            =     y
						for step in range(__lowerCamelCase   ):  # noqa: B007
												__magic_name__            =     a * a - b * b + x
												__magic_name__            =     2 * a * b + y
												__magic_name__            =     a_new

												# divergence happens for all complex number with an absolute value
												# greater than 4
												if a * a + b * b > 4:
																		break
						return step / (max_step - 1)






def _lowerCAmelCase	(  __lowerCamelCase:float   ):

						'''simple docstring'''






						if distance == 1:
												return (0, 0, 0)
						else:
												return (2_5_5, 2_5_5, 2_5_5)






def _lowerCAmelCase	(  __lowerCamelCase:float   ):

						'''simple docstring'''






						if distance == 1:
												return (0, 0, 0)
						else:
												return tuple(round(i * 2_5_5   ) for i in colorsys.hsv_to_rgb(__lowerCamelCase ,						1 ,						1   )   )






def _lowerCAmelCase	(  __lowerCamelCase:int = 8_0_0 ,						__lowerCamelCase:int = 6_0_0 ,						__lowerCamelCase:float = -0.6 ,						__lowerCamelCase:float = 0 ,						__lowerCamelCase:float = 3.2 ,						__lowerCamelCase:int = 5_0 ,						__lowerCamelCase:bool = True ,						):

						'''simple docstring'''






						__magic_name__            =     Image.new("RGB" ,						(image_width, image_height)   )
						__magic_name__            =     img.load()

						# loop through the image-coordinates
						for image_x in range(__lowerCamelCase   ):
												for image_y in range(__lowerCamelCase   ):
																		# determine the figure-coordinates based on the image-coordinates
																		__magic_name__            =     figure_width / image_width * image_height
																		__magic_name__            =     figure_center_x + (image_x / image_width - 0.5) * figure_width
																		__magic_name__            =     figure_center_y + (image_y / image_height - 0.5) * figure_height

																		__magic_name__            =     get_distance(__lowerCamelCase ,						__lowerCamelCase ,						__lowerCamelCase   )

																		# color the corresponding pixel based on the selected coloring-function
																		if use_distance_color_coding:
																								__magic_name__            =     get_color_coded_rgb(__lowerCamelCase   )
																		else:
																								__magic_name__            =     get_black_and_white_rgb(__lowerCamelCase   )

						return img


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			# colored version, full figure
			lowercase    			=       get_image()

			# uncomment for colored version, different section, zoomed in
			# img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
			# figure_width = 0.8)

			# uncomment for black and white version, full figure
			# img = get_image(use_distance_color_coding = False)

			# uncomment to save the image
			# img.save("mandelbrot.png")

			img.show()



