@tomleslie You're right that I was too quick to say that those were the first 10.

@ETM1697 So, does f[x] mean the derivative of f with respect to x?

The comment below pertains to the originally posted form of the equations:

Your formulas are not clear enough. Obviously, they weren't given to you in the form above in your instructions. Please use square brackets to indicate subscripting, for example, the left side of the first equation almost certainly should be x[i+1]. I think that you're missing paretheses also. And why do you have both asterisks and centered dots? Do they both represent multiplication?

@Joe Riel I think that what he wants is a programmatic control so that his program's output appears in an otherwise empty window. Unless his output is strictly a plot, this'll require either some sort of embedded component or a Maplet.

All of your functions are functions of a single variable, so it's not clear what you mean by 3D. They could be done as a single 2D plot if you want.

@DSkoog wrote:

• I do often see a lot of other stack users redirecting questions to MaplePrimes when an 'expert' answer is required, which speaks volumes about our community here.

I think that that's almost always me who says that. There are several reasons that I might say that:

1. Yes, I know that there are some experts on MaplePrimes who aren't answering Questions on math.stackexchange or stackoverflow. (Please let me if there are other StackExchange sites where Maple is discussed.)
2. I may see that the Question is primarily about Maple rather than about math or programming. The moderators are very strict. If the discussion becomes primarily about Maple, it gets shut down, usually within hours.
3. Indeed, I often write that because the discussion has already been shut down by the time that I see it. At that point, Answers aren't allowed, but Comments are, so I put in a Comment like that.
4. I'd like to Answer the Question by displaying a worksheet.
5. StackExchange sites are strictly Q&A. There's not much room for the back-and-forth discussion that's often needed to reformulate the Question, nor is there much room for followup questions. A Comment on a StackExchange site is very limited is size and 2D display ability.

So, while an exclusively Maple site would be a welcome addition to the StackExchange portfolio, such a site couldn't be a replacement for MaplePrimes. What I want is for MaplePrimes to adopt the look and feel of a StackExchange site while still being MaplePrimes: There'd still be Posts and room for extensive back-and-forth discussion. By look and feel I mean the fonts, spacing, clickable controls, notifications, timers, and indexing, among other things.

@nm Of course I have thought of that, and I've looked into it a little. IIRC, they require a core group of at least 200 dedicated and regular users. I'd guess that we have about 30-40 here. Nonetheless, I could submit a proposal and see how many votes it gets. 

An aspect that would require some expert programming is the displaying of uploaded worksheets.

Update: It seems that the core group of 200 users is no longer a requirement. The requirements are in the link that dskoog posted immediately above.

@johan555 Is your expession derived from a norm by Maple, or by hand?

If DirectSearch:-GlobalOptima is returning a negative value, then you should be able to take the evaluation point that it gives you and easily check that all constraits are satisfied and that the function value is negative. I suspect that you are missing a constraint. 

@AmirHosein Sadeghimanesh 

Why not just switch to 1D input?

@Joe Riel Why is it safe in this case to use a remember table with mutable arguments such as records (which are a form of module)?

@Mac Dude I can assure you that the declaration

uses TT= TypeTools;

works. It produces more-readable code than

uses TypeTools;

because a reader reading AddType wouldn't necessarily know that that comes from the TypeTools package, but by TT:-AddType, they would know.

A ModuleLoad procedure can be defined anywhere before its invocation, either in the module's declarations or body, but its invocation (or any procedure's invocation for that matter) must appear in the body.

@Joe Riel The OP hopes to replace run with a serious procedure; they just want to get this Profiling wrapper working before including the actual procedure, which I suspect is an implementation of Zassenhaus's algorithm for factoring polynomials over the integers.

Doesn't profiling essentially rewrite the procedure, similar to what trace does? I wouldn't be surprised if there's some funny business with a module trying to rewrite itself.

@sand15athome It is clear from the early-termination rule for and and andmap (also called the McCarthy rule) that Joe's procedure will be much faster than mine if the difference between the tables is found early. The one to use should be determined based on what you expect the average case to be: equal tables or unequal tables.

@vv I'm not sure about the exact definition of "parse" as opposed to the other levels of interpretation. Yes, the syntax of the inner procedure is checked when it's originally entered. But the assignment := is not done; the experiment that I suggested with print will prove that. There's some subtler stuff that happens between the syntax checking and the assignment. I believe that that stuff is done on the initial entry for a module, but at the execution time for a module.

Is there some reason that you object to a module?

It's a good Question. Vote Up. I've tried several things with your code, but I haven't figured out anything.

Something that seems weird to me is having option object and also returning thismodule. However, this isn't the cause of your error. If you haven't already, I suggest that you read chapters 8 and 9 of the Maple Programming Guide. It's available in the in-app help: just enter ?ProgrammingGuide. However, I find these chapters somewhat sketchy, and the only other option for help is asking here. I consider MaplePrimes members Joe Riel and Acer the world's best public source of information on these module subtleties.