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Plot[] of smooth function results in wildly fluctuating graph?

Hi everybody,

I have a problem with Plot[]. In my code I generate a sequence (in k)
of functions s -> v[k,s] where each of them is piecewise defined on
[a,Infinity) (a>>0) using v[k,s_]=Evaluate[Boole[a<=s<=x1]*(<formula1>)
+ Boole[x1<s<=x2]*(<formula2>) + ... ]. Each of the formulas on a
subinterval is of the form

s^b * \sum_{m=0}^n c[k,m]*(Log[s])^m + linear function

where b is typically something like 50 or -50 and the n (different for
the different subintervals) lies somewhere between 0 and k.

The problem is that after some runs, say when k=20, making a plot of
this function simply by Plot[v[k,s], {s,a,10}] shows wild fluctuations
and absurd values in those subintervals where n is big, while directly
evaluating the function at some points in those subintervals using
N[..] shows that this function (as expected) is actually smooth and has
much smaller values than the plot indicates.

I could of course do soemthing like ListPlot[Table[...]] but that is
unsatisfactory and just not smooth enough. Is there a way to get Plot[]
to use a different way of evaluating the function (I guess the error
must be in there) in order to get a good result?

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