= Solution
The <affine space> $X=\mathbb A^n_k$ is an <integral scheme>, hence its underlying <topological space> is irreducible. Every nonempty open subset of an irreducible <topological space> is irreducible and in particular connected. A section of the <constant sheaf> with value the <function field> $K=k(t_1,\ldots,t_n)$ is a <locally constant function>, so on any such open subset it is constant. Thus its sections are $K$ on each nonempty open subset and zero on the empty set. All restriction maps are either identities on $K$ or maps onto zero.
The <constant sheaf> is therefore a <flasque sheaf>. It has its natural $\mathcal O_X$-<module> structure because a <regular function> on a nonempty open subset embeds in the <function field> and acts by multiplication. Part (i) now gives
$$
\boxed{H^0(X,\mathcal F)=K,\qquad H^p(X,\mathcal F)=0\quad(p>0).}
$$
This is an instance of <constant sheaves on irreducible spaces are flasque>; no restriction on $n$ is needed.
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