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These are answers submitted by Werner

Look for interpolation in the CurveFitting package. Regards WW
plot([fct1(x),fct2(x),x=a..b]); Note the position of the brackets [] ! Regards WW
If you use cubic splines then Simpsons rule (on each interval) then not-a-knot boundary conditions yield the best result in that sense that the resulting formula is exact for polynomials of degree <=3. Regards === MODERATOR EDIT === I changed the input format of your post to Plain Text so that the less than sign will not interfere with the HTML
It is not easy to give any reasonable advice without knowing the system. One possible strategy could be to find the general solution of the 14 linear equations in 16 unknowns. The solution (if it exists ...) should have two parameters (or more ...); then insert this solutions into the nonlinear equations. Usually you will have to solve the resulting system approximately by a method like Newton's; in special cases -but rather unlikely- there is an symbolic solution which could be found by Maple's solve command. But as I said in the introduction: Things heavily depend on the concrete situation. Regards WW
Maybe a starting point is my contribution "Symbolic computation of Fourier Series" in the application center (http://www.maplesoft.com/applications/app_center_view.aspx?AID=185) . Use the maplet builder to generate the maplet for input and output. Regards Wilhelm
plot([10,y,y=-5..5]); Regards WW
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