@nMaple 

Apparently the conversion from Heaviside form to abs form doesn't work in Maple 17, no matter what assumptions I make. But a conversion to piecewise form does work, and int is able to integrate it. So, for Maple 17 (and probably earlier), use

convert(int(convert(f(t-q)*g(q), piecewise, t), q = -2 .. 10), Heaviside);

Regarding the integral's value for t < -2 and t > 10: Yes, the integral is 0 for t < -2, but it has a constant value of 45 for t > 10.

Regarding copy-and-pasting in plaintext: There are several ways, but my recommended way is to code in plaintext in the first place. This means using character style Maple Input rather than 2D Input. The character style is the leftmost pull-down on the last row of toolbars. You can set this style as your default by using the Tools -> Options menu (any many of the oldtimers here on MaplePrime would recommend that you do so).

@vv Your English is good, and I didn't suspect that you weren't a native speaker.

I think that the intended meaning of "the number 123 has three distinct digits" is clear to anyone who uses base-10 arithmetic by default---which means any native English user since our number words are base ten---and such usage would be unlikely to raise an eyebrow except perhaps from the nuns at my elementary school. However, I believe that such usage is technically incorrect. Some corrected versions include

• The numeral 123 has three distinct digits.
• The number 123 has three distinct digits in its base-10 representation. 

The key distinction to me is that a number is an abstract entity which exists regardless of whether it's written down or spoken. A numeral is a symbol representing a number. (So one hundred twenty-three, 123, and CXXIII are all numerals for the same number.) A digit is one of the symbols used for the coefficients in a positional arithmetic system. A Hindu-Arabic digit is one of the specific symbols 0, 1, ..., 9.

@H-R I agree wholeheartedly with vv on this matter. In particular, 

• Attempting to write a CAS restricted to the real-number system but which still has all the power of Maple for working within the real numbers seems to me to be a momumental task, if it's possible at all.
• Ignoring complex numbers is pedagogically unsound. For example, teaching that int(1/x, x) = ln(abs(x)) is an abomination. And I would've mentioned vv's arctangent example had they not done so already.

However, I see no problem with wanting to assume that variables are real! That's a different issue. The heart of the problem in this Question is that RealDomain ignores additional assumptions. My guess is that it wouldn't be so difficult to modify the package so that it would allow additional assumptions.

In Maple, any assumption where a variable appears on one side of a directional inequality automatically assumes also that that variable is real. In this Question, it's essential to assume u > 1 for the desired simplification to occur. Thus there's no need to assume that u is real---that's done automatically.

I do appreciate that you'd like to assume that all user variables are real without having to list them all. I think that that would be an easy thing for Maple to implement. It'd be something different from the RealDomain package.

There are several contexts already in Maple where it's assumed that all user variables are real. Two general ones are evalc and assuming real. You can append the phrase assuming real to any command without mentioning any specific variables.

In English, there are the words number, numeral, and digit---which have distinct definitions. The number 3 occurs only once in the sequence of positive integers from 1 to 1000. The digit 3 occurs 300 times in the base-10 numerals for that sequence. Of those numerals, 271 contain the digit 3.

So I suspect that the usages of number in the Question need to be adjusted.

@nMaple If you upload an executed worksheet showing my command not working, then I may be able to suggest an adjustment. Please start your worksheet with the commands

restart;
kernelopts(version);

You can upload a file by using the fat green uparrow on the toolbar of the MaplePrimes editor. Rouben's admonishment about pictures versus plaintext doesn't apply to uploaded worksheets.

@tomleslie wrote:

...but assuming that 'classic' gives the same functionality....

That assumption is really, really far from reality. There is no Tools menu. The equivalent of Options is File->Preferences. It has no Interface tab. There is no Large Toolbar Icons checkbox.

@H-R You can do computations with reals in Maple. The way to do it is (generally) to use assume and assuming, not RealDomain. I think that the problem with RealDomain is simply its name, which makes people think that its purpose is to restrict computations to the reals. It should be named Student:-Precalculus:-RealDomain. Had it been named thus, you wouldn't have used it, right?

@vahid65 Try copy-and-pasting my code rather than retyping it. I think that you missed a comma between t= -6*Pi..Pi and thickness= 3. If you encounter any more errors, you'll need to upload an executed worksheet showing the error message. Use the fat green uparrow to upload a file.

@Feenix 

What do mean by your title "It is doesnt work"?? If it doesn't work, then you need to show what you got when you used it, so that I can attempt to fix it. It worked for me (in Maple 18).

My name is Carl Love, exactly like my avatar.

My Answer assumes that you simply want to remove or discard any solution sets that contain RootOf. Doug Meade's Answer assumes that you want to reprocess the RootOfs into more-standard algebraic forms and then discard any nonreals. It's not clear to me which of these alternatives you want. Doug's Answer seems to me the more-usual request, but my Answer seems to correspond more closely to the actual wording of your Question: "remove Complex and RootOf from this list".

@tomleslie Thanks for the correction, and I corrected the original.

@vv It's an excellent question that I don't know the answer to. My knowledge about the matter is pretty much limited to what I've gleaned from the help pages ?Heaviside, ?NumericEvent, and ?NumericEventHandler. I think it'd make a good thread-starting Question.

Essentially the same question applies to signum(0).

@nMaple Then your use of NumericEventHandler is appropriate. It will affect the evaluation of the resulting function, but I don't think that it'll affect the ability of int to find the symbolic integral. I'm not sure about that last part; anyway, the solution with convert works regardless of NumericEventHandler.

@vv 

'f()' $ 5;

No index variable is needed.

@tomleslie If you're attempting a numeric integration of an analytic integrand over a finite hyperrectangle and it returns unevaluated, that almost certainly means that you need to adjust epsilon, Digits, or digits or some subset of those. If you're using one of the four cuba methods, you may also adjust absepsilon and maximalpoints.

By setting infolevel[`evalf/int`]:= 4;, you can often get some hints on how much adjustment is needed.

@Markiyan Hirnyk What is the signifiicance of your epsilon= .2? That's means not even one significant digit.