I haven't seen any applications that justified going higher than 6th order, but my experience is in the chemical industry.  It's not free, but JMP (Jump) by SAS will probably do it.

Good luck,
Latexman

As a general rule, you need to be very careful when fitting high-order polynomial curves of best fit, as they can duck and weave all over the place between your data points.  And as for using them for extrapolation, be ultra-very careful.  Personally, I shy away from using any polynomial higher than a cubic.

If you feel you need to resort to a high-order polynomial, your data might actually be telling you that a polynomial is not appropriate.  You might be better off fitting some different form of curve - reciprocal, exponential, etc - or even a combination of these.  The resulting curve fitting cannot be done automatically within Excel, but it is not difficult.  By laying your data out in an appropriate manner you can set up a cell that contains the sum of the squares of the errors for any particular set of parameters for the hypothesized relationship.  You can then use the Solver to search for the set of parameter values that minimizes this sum of the squares of the errors.

Also, look very hard at your data, and ask yourself if there are any a priori  reasons for expecting any particular behaviours (such as asymptotes), even if these behaviours will not significantly manifest themselves within the range of your data points.  If so, select a form of curve that honours these behaviours.

HTH

It is possible:put your independent variables in a column, say "A"; their squares in column "B", their cubes in column "C" and so on.... and in the last column put your dependent variables. Apply tools.Data Analysis.Regression, select ranges,go and you will get coefficients of the terms as you wrote them preceeding by a constant.But before you do it please read the answer of Denial at least two times!
m777182

Thanks everyone.
I finally found a way to represent my curves as fourier series equations (by setting up composite tables in Excel) rather than polynomials and have a much better approximation. The area under each curve was also obtained using approximate integration methods.
Thanks a lot for your contributions.

Kokonut