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Question: high precision problem

Question:high precision problem

maple fan 205 Maple
digits evalf
April 03 2015
0

I found this problem in a book about mathematica.
I want repeat it with maple.
But even Digits=1400, the exact value of s@x=70 is still different with the result(0.633319) on that book.
How to resolve this problem?
I want some help.

code:
restart;
Digits:=1400:
p:=convert(series(cos(x),x,201),polynom):
s:=add(op(i,p),i=[1,2,3,-1,-2,-3]);
add(evalf(coeff(p,x,i))*70^i,i=[200,198,196])+add(evalf(coeff(p,x,i))*70^i,i=[2])+add(evalf(coeff(p,x,i))*70^i,i=[4]);
#plot(s,x=0..40,view=[0..40,-2..2],numpoints=6000,gridlines,style=point);
simplify(eval(s,x=70));
evalf(%);
Please Wait...