These functions compute integer multiples of alpha near to x

Floor returns the greatest integer multiple of x less than or equal to alpha

Ceil returns the least integer multiple of x greater than or equal to alpha

Round returns the integer multiple of alpha nearest to x

Trunc returns $\mathrm{trunc}\left(\frac{x}{\mathrm{\alpha }}\right)·\mathrm{\alpha }$, i.e. whichever of the Floor or Ceil that is closer to 0.

All these functions call their lowercase name equivalents on $\frac{x}{\mathrm{\alpha }}$ and so behave the same for nonreal, and nonconstant values of x. See trunc for those details.

$\mathrm{Trunc}\left(75341\,1000\right)$

$75000$

$\mathrm{Ceil}\left(75341\,1000\right)$

$76000$

$\mathrm{Trunc}\left(-75341\,1000\right)$

$\mathrm{-75000}$

$\mathrm{Floor}\left(-75341\,1000\right)$

$\mathrm{-76000}$

$\mathrm{Floor}\left(-75341\,-1000\right)$

$\mathrm{-76000}$

$\mathrm{Round}\left(11.1\,\mathrm{\pi }\right)$

$4\mathrm{\pi }$

$\mathrm{Floor}\left(\mathrm{sqrt}\left(3\right)\,\frac{\mathrm{\pi }}{4}\right)$

$\frac{\mathrm{\pi }}{2}$

$\mathrm{Ceil}\left(14\mathrm{Unit}\left(m\right)\,\mathrm{Unit}\left(\mathrm{inches}\right)\right)$

$552⟦\mathrm{in}⟧$

$\mathrm{Floor}\left(x\,10\right)$

$10⌊\frac{x}{10}⌋$

$\mathrm{Floor}\left(x\,-10\right)$

$10⌊\frac{x}{10}⌋$

$\mathrm{Floor}\left(10\,x\right)$

Error, (in Floor) invalid input: 2nd argument, alpha, expected to be a real number with or without a unit but received, x

The Trunc, Round, Floor and Ceil commands were introduced in Maple 2025.

For more information on Maple 2025 changes, see Updates in Maple 2025.