@Mikael Hakman Nonetheless, if the OP could provide me with such a trivial example, I could extend it to the case where g can't be inverted. 

Would you please provide a simplified example of what you want, i.e., an example where g can be symbolically inverted? If you can do that, then I can show you how to extend it to cases where g can't be symbolically inverted. As it stands, I can't see how what you want is any different from a parametric plot. 

Showing the curve, the tangent line, and the point (a, f'(a)) together on one plot makes no sense. Are you sure that you don't mean the point (a, f(a)), the point where the tangent line touches the curve? 

@anton_dys The reason that I used eval is that it would adequately handle the cases where dsolve returns several functions in one solution. You can't do that with rhs. Your solution also has the flaw that it causes the dsolve to be executed every time u is invoked. You must use unapply to avoid that. 

What's the program supposed to do if the byte is greater than 7 after the random bit is flipped? 

@acer Thanks for those answers. Now some more-serious questions about objects (for my learning).

In your module above, what would cause ModuleCopy to be invoked, and what would determine the number of arguments that it had?

Where is it specified that the magnitude is the left operand and the argument the right operand?

Can invocations of `&angle` within the module be replaced with ModuleApply?

Why doesn't `*` contain an if nargs=1 then return args[1] clause as appears in `+`?

@acer Yes, put it on the Application Center. It's a great example of an object and of user-defined binary infix operators.

What can be used as a binary infix operator? anything that starts with &? Does that include Greek letters like `ε`? Is it possible to use such in 1D input without quotes, or would the semicolon mess things up?

Please try attaching that worksheet again.

@acer You're right: "Separately summing" was a poor choice of words. But I still think that the title "Separation of even and odd terms suffices" applies. Note that your accelerator procedure F only works when the chunksize is even.

@acer Aha! That gives me an idea of something even easier. Since the even and odd terms both form decreasing sequences, since each is asymptotic to a convergent p-series, and since the numeric summer only looks at the numeric values of the terms, separately summing the even and odd terms should do it.

Using the general series term F(n) from my previous Answer,

evalf(Sum(F(2*n)+F(2*n-1), n= 1..infinity));

     0.785852250894067

Voila. This also confirms the accuracy of the asymptotic series approach, although it was a much bigger hammer than was necessary for the job.

It's tricky. You essentially have to do it one procedure at a time. I have posted code here in the past which will cycle through all the procedures in a module and print them. However, the search tools on MaplePrimes are atrocious, and I can't find that post. Perhaps someone else can. (*)

Some modules have a "module body"---a small section of directly executable code. There is no way to see this code as it's not even saved with the module. This code is usually irrelevant and I think that it's unlikely to be used in a saved package anyway.

((*) Let me take this opportunity to request again from the MaplePrimes administrators: Please, please make this entire site searchable by Google, with the pointers pointing to the threads rather than to the users' Answers and Replies sections!! When a user has over 5000 Answers and Replies (as I do), a pointer into those sections is worthless!! What's stopping you from making this change? Wouldn't it require only a trivial amount of effort? There's a vast storehouse of Maple knowledge here that's essentially going to waste. ) 

@acer However, the infinite sum, although correctly entered, can't be evaluated under evalf. I'm working on an approximation based on asymptotic expansion. There are a few snags.

@YasH Without the parse, the cat(L[]) produces a variable name that looks like a number. You will notice that the result shows in italics in the GUI. With the parse, you actually get a number, which shows in an upright font.

(This may have changed in a recent version of Maple. I'm stuck with Maple 16 today.)

@JessyOw I think that you need to enter the string with quotes: `Hello! Bob` rather than Hello! Bob.

On the other hand, I do have sympathy for the other position: that the condition number is a precisely defined mathematical entity and that ConditionNumber should respect that. So perhaps the other number should be relegated to a command ConditionNumberEstimate or some such. And since this estimate is so crude, perhaps only its ilog10 should be reported.