This problem can be found in Purcell's Calculus. "Find the formula and plot the accumulation function A(x) of the indicated area". Can you write the accumulation formula without using calculus and without piecewise-defined function ?.
math for fun
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Are we allowed to use the floor function or the absolute value function? If so then it's really easy to make a function that hides it's piece-wise definition through the use of other functions.