Squary Polynomial

Algebra Level 4

Let $f(x)$ be a monic quartic polynomial such that ,

$f(0.5)=\frac{25}{16}$

$f(0.\overline{3})=\frac{100}{81}$

$f(0.25)=\frac{289}{256}$

$f(0.2)=\frac{676}{625}$

Evaluate : $\phi \left (f(10)+f(9) \right )$