Let a, b, c ∈ R. If f(x)= a x^2+ b x+ c is such that a + b + c =3 and f(x+y)=f(x)+f(y)+x y, ∀ x, y ∈ R, then Σ_n =1^10 f( n ) is equal to:

Let $\displaystyle \mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{R}$. If $\displaystyle f(x)=\mathrm{a} x^2+\mathrm{b} x+\mathrm{c}$ is such that $\displaystyle \mathrm{a}+\mathrm{b}+\mathrm{c}=3$ and $$f(x+y)=f(x)+f(y)+x y, \forall x, y \in \mathbf{R}, $$ then $\displaystyle \sum_{\mathrm{n}=1}^{10} f(\mathrm{n})$ is equal to :