Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 transitive v. To determine by mathematics, especially by numerical methods: computed the tax due. See Synonyms at calculate.
 transitive v. To determine by the use of a computer.
 intransitive v. To determine an amount or number.
 intransitive v. To use a computer.
 intransitive v. Informal To be reasonable, plausible, or consistent; make sense: Your alibi doesn't compute.
 n. Computation: amounts beyond compute.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 v. To reckon or calculate.
 v. To make sense.
from the GNU version of the Collaborative International Dictionary of English
 transitive v. To determine by calculation; to reckon; to count.
 n. Computation.
from The Century Dictionary and Cyclopedia
 To determine by calculation; count; reckon; calculate: as, to compute the distance of the moon from the earth.
 Synonyms Reckon, Count, etc. See calculate.
 To reckon; count.
 n. Computation.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 v. make a mathematical calculation or computation
Etymologies
Examples

Obviously the one thing that Wolfy can't compute is how to have sufficient servers to handle it's user load. palmerkun jthatch
First Look At Wolfram Alpha’s Impressive Knowledge Computation  Lifehacker Australia

You'll probably find (after you spend some time here) that most of us started in Linux because we were looking for a better way to "compute"  we started dualbooting Windows and Linux, but started booting the Linux side more and more often, simply because we can use our machines rather than just having to maintain them all the time.

103 His malady increased, and after a dysentery which continued three days, he expired in the palace of Ravenna, in the thirtythird, or, if we compute from the invasion of Italy, in the thirtyseventh year of his reign.

We’ll be able to compute from the knowledge that our civilization has accumulated.
Wolfram Blog : Stephen Wolfram on the Quest for Computable Knowledge

What doesn’t quite compute is that the robot goes to all this trouble to look and breath like a sex kitten, but the speech is very mechanical in some parts.

Senator DEBBIE STABENOW (Democrat, Michigan): At a time when people are losing their jobs, working parttime jobs, seeing their wages go down, and the incomes of the wealthiest 400 people in the country have gone up about 400 percent in the last decade and a half and their tax rates have been cut in half, for the majority of Americans that doesn't compute, that is just not fair.

And to compute is to collect the sum of many things added together at the same time, or to know the remainder when one thing has been taken from another.

In fact, they are starting to behave like the device that neurons use to compute, which is called an ion channel.

If we are specially referring to a compute instance shares much of the same characteristics of the server it would run if it were on premises.

"At a time when people are losing their jobs, working parttime jobs, seeing their wages go down, and the incomes of the wealthiest 400 people in the country have gone up about 400 percent in the last decade and a half and their tax rates have been cut in half, for the majority of Americans, that doesn't compute, that is just not fair," the Michigan Democrat said.
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