Inductive reasoning is not a mechanism for mathematical proof, and is not mathematical induction. Something's very wrong if one ever mixes those up together in the same context.

A mathematician should not consider that "..it is sometimes very easy to believe induction is sufficient proof...", where the context qualifies that as inductive generalization or "inductive reasoning". 

@David1 

Download trigoac.mw

@tomleslie The worksheet was already there, a few hours before your last claim that it hadn't been uploaded. All you had to do was look. How hard can that be?

(This is the brusque way you often address people here.)

I should also mention the following mechanism (which I often reach for instead of unapply, because it has some more general uses):

Here, the Maple kernel replaces the formal parameter n (of the procedure) for the name n in the expression, when it forms the procedure body.

I also have the choice to declare local x in the template of the procedure body. That can be valuable. (These procedures bar will otherwise pick up any assigned value of x at the higher level from which bar gets called, typically resulting in a run-time error.)

Download subs_proc.mw

When you lprint the Array it does not show the entries whose value are zero (because that is the default value).

@taro 

Download cyl.mw

@Carl Love Good idea. I think I got confused about the question, and was thinking of function calls instead of stored structures.

You might have a look at these profiling mechanisms.

I'm not sure offhand what special support -- if any -- there might be for records or static methods of objects. I find it mostly useful for profiling my "Library level" interpreted procedure calls/usage. The CodeTools functionality is newer.

https://www.maplesoft.com/support/help/Maple/view.aspx?path=CodeTools/Profiling

https://www.maplesoft.com/support/help/Maple/view.aspx?path=exprofile

Do you mean that the Matrix appears as 2D Output, or was it inserted as 2D Input by using the Matrix Palette?

If the problem is with the Matrix as typeset 2D Input then does it work if you hit Enter and then try it on the output?

Why not upload a Worksheet or Document that exhibits the problem?

@vv That's nice. Here are a few more ways to accomplish those things -- and a few comments if I may add them -- using that generated f .

These following operator form calls work as they ought to.

int(f, 0..Pi, numeric);
evalf(Int(f, 0..Pi));
int(f, 0..evalf(Pi));

It's clearly a bug that evalf(Int(f(x), x=0..Pi)) does not work, while something weird like evalf(Int(''f(x)'', x=0..Pi)) does produce the float result.

It's unfortunate that D(f) has not yet been taught to return unevaluated, since the hook from evalf(D(...)) into fdiff is a useful syntax. Hopefully someone will fix that in D.

The first of these ideally would work as just evalf(D(f)(2)) . And the third of these ideally would not need the uneval quotes.

evalf(D(t->f(t))(2));
fdiff(f(x), x=2);
evalf(eval(diff('f'(x), x), x = 2));

Similarly, these would look nicer working with just D(f) instead of D(t->f(t)) .

plot([f, D(t->f(t))], 0 .. 10);
plot([f(x), D(t->f(t))(x)], x = 0 .. 10);

As a side note, these both compute without an error message.

fsolve(f, Pi/2..3*Pi/2);
fsolve(f(x), x=Pi/2..3*Pi/2);

And these first two calls succeed, but unfortunately the third emits an error message.

Optimization:-Maximize(f(x), x=0..Pi);
Optimization:-Maximize(t->f(t), 0..Pi);
Optimization:-Maximize(f, 0..Pi);

I suspect that some of these problematic cases relate to appliable modules more generally, and not just to Interpolation objects.

@AliahNiu The image shows {sin(x)}^(d-2) as part of the integrand, which is not valid syntax since the curly braces denote a set. That should be sin(x)^(d-2) .

Christopher2222, please upload the actual .mw file from which you are trying to retrieve the value associated with the "L1" label.

Then tell us exactly which platform you're using, eg. Windows 7 32bit , or Windows 10 64bit , etc.

@Earl Mapleprimes won't let me download those last two attachments, in your Comment immediately above. Could you try uploading them again, without the ampersand in the file name?

@tomleslie I was going to mention this alternate command yesterday, but found it a bit brittle (and not quick). 

Of 800 files collected from Mapleprimes it failed with some error on about 70.

And in at least three cases it failed with an infinite recursion error, which is not catchable and thus stopped my script outright. Ie. it stopped the loop over all the files. I had to remove those filenames from the list and re-run.

Of course it may well work for all of the OP's files.

@tomleslie Does your approach detect the instance of

  with(plottools)

in that second attachment he gave?

I mean, his attachment as is, last saved in Maple 2016 (and running the detection script in Maple 2016 too, though I doubt that would affect it).