From Example 6.7.1, $\mathrm{\λ}\=5.078061188$, and rounded to four decimal places, $\mathrm{\λ}$ becomes $\stackrel{\^}{\mathrm{\λ}}\=5.0781$. By trial-and-error, the smallest value of $n$ in Simpson's rule for which the approximation to the integral rounds to $\stackrel{\^}{\mathrm{\λ}}$ is $n\=10$. Simpson's rule with this partition returns $5.078118675$, which rounds down to $\stackrel{\^}{\mathrm{\λ}}\=5.0781$.

The  tutor could be used to implement Simpson's rule for different values of the partition $n$. Alternatively, the ApproximateInt command can be use, as in Table 6.7.5(a).