To solve the integral of $f(x) = x^2$ over the interval $[1, 4]$ using Simpson's 3/8 rule, we must first confirm the number of subintervals (n) and then apply the rule.

However, it seems like there's some confusion with the value given for $n$. Simpson's 3/8 rule requires $n$ to be a multiple of 3. You mentioned $n = 0.5$, which doesn't align with this requirement. Typically, $n$ is the number of subintervals, not the size of the step. Could you please clarify if $n = 0.5$ was meant to represent the step size $h$ instead?

If the intention was to use $n = 3$ subintervals, I can proceed with the calculation. Let me know how you'd like to proceed.