Higher Order Functions used for simulations of dice rolls. Definition: An n-sided dice function takes no arguments and always returns an int from 1 to n, inclusive. Types of n-sided dice functions: - Randomized: a randomized dice function can be fair, meaning that ir produce each possible outcome from 1 to n with equal probability. Examples: four_sided, six_sided - Deterministic: a deterministic dice function will be used for testing. Deterministic test dice functions always cycle through a fixed sequence of n values. - We write a make_fair_dice higher-order function to return a fair, randomized n-sided dice function. - We write a make_test_dice higher-order function that will return a deterministic, testing n-sided dice function.

Write a program that displays the following menu: geometry calculator 1. calculate the area of a circle 2. calculate the area of a rectangle 3. calculate the area of a triangle 4. quit enter your choice (1-4): if the user enters 1, the program should ask for the radius of the circle and then display its area. use the following formula: area = ď€(the square of r) use 3.14159 for ď€ and the radius of the circle for r. if the user enters 2, the program should ask for the length and width of the rectangle and then display the rectangle’s area. use the following formula: area = length * width if the user enters 3, the program should ask for the length of the triangle’s base and its height, and then display its area. use the following formula: area = base * height * .5 if the user enters 4, the program should end. input validation: display an error message if the user enters a number outside the range of 1 through 4 when selecting an item from the menu. do not accept negative values for the circle’s radius, the rectangle’s length or width, or the triangle’s base or height. note: if the user enters an improper menu choice (1-4), the program prints "the valid choices are 1 through 4. run the program again and select one of those." if the user enters a negative radius, the program prints "the radius can not be less than zero." if the user enters a negative value for height or base, the program prints "only enter positive values for base and height."