Engineer the next era of AI

A newly born magnetar is modeled as a rigid biaxial body whose principal moments of inertia are $I_1 = I_2 = I(1-\varepsilon)$ and $I_3 = I$, with $I = 1.50 \times 10^{45}\,\mathrm{g\,cm^{2}}$, $\varepsilon = 6.00 \times 10^{-3}$, and stellar radius $R = 1.20 \times 10^{6}\,\mathrm{cm}$. The star rotates rigidly about a fixed axis $\hat{z}$ at angular velocity $\Omega = 2\pi/P$, and its deformation symmetry axis $\hat{e}_3$ is held at a constant wobble angle $\theta_w = 20.0^{\circ}$ from $\hat{z}$, sweeping a cone about $\hat{z}$ at rate $\Omega$. Gravitational radiation is computed from the Einstein quadrupole formula $$L_{\rm GW} = \frac{G}{5c^{5}}\left(\dddot{Q}_{ij}\,\dddot{Q}_{ij}\right)_{\rm avg}.$$ The star also spins down by magnetic dipole radiation with polar surface field $B_p = 5.00 \times 10^{13}\,\mathrm{G}$ and magnetic obliquity $\alpha = 60.0^{\circ}$, for which $$\dot{J}_{\rm dip} = -\frac{2B_p^{2}R^{6}\sin^{2}\alpha}{3c^{3}}\,\Omega^{3}.$$ Take $J = I\Omega$ and $\dot{J}_{\rm GW} = -L_{\rm GW}/\Omega$, with the two torques acting additively. Determine the total energy radiated in gravitational waves as the spin period evolves from $P_0 = 3.00\,\mathrm{ms}$ to $P_f = 6.00\,\mathrm{ms}$, in erg, to 3 significant figures.