> I'm on Maxima 5.19.2 and I get the same result.
> With setcheck set to true I see:
>
> (%i10) sum(d(k),k,0,a);
> k SET TO g16510
> (%o10) a+1
>
> what does g16510 stand for?
That is a gensym - a symbol guaranteed to be unique. And since d() is
passed this symbol and not numbers it always evaluates to 1 and never
to 0. So this explains the +1 too...
> Moreover, doesn't Maxima knows about Gauss' formula?
>
> (%i11) sum(x,x,1,n);
> (%o11) 'sum(x,x,1,n)
>
> Maxima returns a noun form, instead of n*(n+1)/2
Read the documentation about simpsum.
HTH,
Harald