A car travels along a piecewise-defined path. The distance it covers every hour is described by the function:
\[d(t) = 
\begin{cases} 
10t + 5 & \text{if } 0 \le t \le 3, \\
25 & \text{if } 3 < t \le 6, \\
15t - 30 & \text{if } t > 6.
\end{cases}
\]
If the car travels for a total of 8 hours, find the total distance covered by the car. Let's think step by step and output the final answer within \boxed{}.
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