According to Table 7.2.1, the arc length is obtained by evaluating the integral ${\int }_{{\mathrm{\theta }}_1}^{{\mathrm{\theta }}_2}\sqrt{r^2\+{\left(r\prime \right)}^2}\mathit{\ⅆ}\mathrm{\theta }$ for $r\=2 a \cos \left(\mathrm{\θ}\right)$. From Figure 7.2.1(a), the diameter of the circle is $d\=2 a$, so the expected value for the arc length is the circumference of the circle, namely, $\mathrm{\π} d\=2 a \mathrm{\π}$. This is indeed the case, as the following integration shows.

In some instances, Maple considers that a definite integral is made "simpler" by evaluation. Here, the evaluation could have been done with the value command under the aegis of the assumption that $a$ is positive. Without this assumption, Maple will return $\mathrm{csgn}\left(a\right)$, that is, the "complex sign" of $a$.

Applying the Simplify option in the Context Panel avoids the need for the commands illustrated below.