Here is a Python program that uses an anonymous function to display the powers of 2 up to a given maximum value:

# define a function to display the powers of 2
display_powers_of_two = lambda max_power: [print(2 ** i) for i in range(max_power + 1)]
# test the function
display_powers_of_two(5)

This program defines a function named display_powers_of_two() that takes a single argument max_power. This argument specifies the maximum power of 2 to be displayed. The function uses a lambda expression to define an anonymous function that computes and prints the powers of 2. The lambda expression uses a list comprehension to compute the powers of 2, which are then printed by the function.

Here is the output of this program:

1
2
4
8
16
32

You can use this program as a starting point and modify it to fit your specific needs. For example, you can change the lambda expression to display the powers of a different number, or you can add more code to the function to perform additional tasks.