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I was trying to evaluate some intergal over some cube with variable side length, but for some reason Mathematica spit out the input. The interand was sufficiently nice that I couldn't believe it didn't have a closed form solution, moreover it took only a few seconds. I thought my syntax was wrong, so I tried integrating the constant 1. And to my surprise it still does not work. If I substitute the side length with a number it works, but for some reason with some paramenter it doesn't. I try using

Integrate[1, Element[{x, y, z}, Cube[l] ], Assumptions -> l > 0]

and it doesn't work, it just answers with the input. If instead I put a number $n$ it gives the obvious correct answer $n^3$. What is happening?

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    $\begingroup$ @tommy1996q, I think you've found another bug. Note Integrate[1, Element[{x, y}, Rectangle[-{l, l}, {l, l}]], Assumptions -> l > 0] and Integrate[1, Element[{x, y}, Rectangle[-{l, l}, {l, l}]], Assumptions -> l > 0] and RegionMeasure[Cube[l]] all work as expected. $\endgroup$
    – Craig Carter
    Commented Jul 7 at 17:55
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    $\begingroup$ Integrate[1,{x,-l/2,l/2},{y,-l/2,l/2},{z,-l/2,l/2}] Then estimate the amount of your time spent fighting how to do all this abstractly versus the amount of your time spent doing this concretely. $\endgroup$
    – Bill
    Commented Jul 7 at 18:00
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    $\begingroup$ @CraigCarter if Mathematica returns an integral unevaluated, that isn't really a bug. It hasn't given you a wrong answer. So I think this is an "opportunity for improvement" rather than a bug. $\endgroup$
    – mikado
    Commented Jul 7 at 19:29
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    $\begingroup$ Use Cuboid instead. Integrate[1, Element[{x, y, z}, Cuboid[{0,0,0},{l,l,l}] ]] (* l^3 *) $\endgroup$
    – LouisB
    Commented Jul 8 at 1:22
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    $\begingroup$ Interestingly: Volume[Cube[l]]gives l^3! $\endgroup$
    – Ulrich Neumann
    Commented Jul 8 at 8:09

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