@John Dolese 

There are many top-level (i.e., non-package) Maple commands for converting to integer: round, ceil, floor, trunc.

The default numbers in Maple aren't floats because conversion from exact results to floats is mostly a one-way process---the floats cannot usually be converted back to exact values. The exact results can always be converted to floats with evalf. There are not many results of substantial mathematical interest that can be proven with floats.

@AngelaRURU 

Go to menu Tools => Options => Precision. The last item is "Limit expression length to...." Uncheck the box. Then click on Apply to Session or Apply Globally.

@Josolumoh 

Please read the help page ?ExportMatrix

The ... wasn't intended to be used literally! It's meant to be filled with other options, which you'll find if you read the help page.

@Josolumoh I gave the ExportMatrix syntax wrong. It should be

ExportMatrix(F, M, ...);

where F is the filename, M the matrix, and ... the other options. See ?ExportMatrix.

@SamNaval That being the case, your differential order is 8: 4 with respect to x and 4 with respect to y. So you need 8 boundary conditions. You only have six.

@Josolumoh What is your Maple version? Also, please post an executed worksheet that contains this erroneous result.

@Josolumoh Suppose that you want to fill an n by m Matrix for export to another package. Then do

M:= Matrix((n,m), datatype= float[8]);
Statistics:-Sample(B1, M, method= [discrete, range= 0..n]);
ExportMatrix(M, ...);

where ... represents whatever ExportMatrix options are appropriate for the target package.

@SamNaval 

In your original differential equation there appears a term w''(x)''(y). I'm not familiar with that notation. Does it mean

diff(w(x,y), x, x, y, y);

?

@Josolumoh Suppose that you want to repeat it m times. Then do

'Statistics:-Sample(B1, 10, method= [discrete, range= 0..n])' $ m;

Note the forward single quotes (aposthropes) surrounding the left part of the command.

@AngelaRURU There is no general technique for it, and no automatic way in Maple. It's a massive area of research. For example, Google "Asymptotic Expansion of Integrals". With four parameters, I don't have much hope for a meaningful expression that approximates your integral.

@vv It is commonplace for numeric procedures to increase the value Digits to whatever is needed to achieve the accuracy specified by the value of Digits in use when the procedure is called. If you need to set

Digits:= ceil(1.6*Digits);

in your procedure, then that's what you should do. Digits is an environment variable, so changes that you make to it are automatically reverted when the procedure is exited. To see examples of how Digits is manipulated, look at the code for any procedure named `evalf/F` where F is any standard mathematical function name.

The solution to your pair of equations eq[1] and eq[2] is indeed (0,0). I haven't checked your calculations before that. You should be using Maple's higher-level commands such as dsolve (for ODEs, BVPs, IVPs, some DAEs) and fsolve (for systems of floating-point algebraic equations).

I don't understand how---if at all---what you're asking for is any different from simply running separate Fit commands to fit x(t) and y(t).

@Markiyan Hirnyk The issue with integration can't be blamed on vv's procedure. It's just the failure of the numeric integrator to increase Digits to the extent needed the achieve the requested accuracy, which occurs in a great many numeric integrations with complicated integrands. Just change the int command to (for example)

int(Cf^2, 0..1, numeric, epsilon= 1e-4);

     0.2999991429

@tomleslie The OP is not redefining the Catalan numbers; the expression that he/she gave is one of many ways that Catalan numbers can be computed. It's mentioned in the Wikipedia article that you cite; it's the third displayed formula on the page.