Exposure Compensation – How can we take a better picture of this creek under a bright sun and dense vegetation on the banks?

If you have a polarizer on your lens, you have to adjust (ie rotate) to achieve the desired effect. That's why you can rotate it in the first place, as opposed to other filters. It can be used to block the polarization of the reflection (making it able to look in the water without reflection) but it can also be used for only admit the polarization of the reflection which maintains the reflection as it is, but reduces the rest of the image by one stop, thus reducing the brightness of the reflection to that of the non-reflected image.

Note that polarization occurs primarily at certain angles, but a typical water surface is a good candidate. A polarizer does not withstand the reflections of a flash (unless you put a polarizing filter on the flash itself) because the problematic reflection direction does not cause polarization.

About flash: With contrasts such as the one presented here, an extra flash at a decent level (-2EV or higher) can do a lot of good for shadow detail without spoiling the character of the scene.

You can also perform "exposure bracketing" by creating 3 photographs at a different exposure and then combining them into a "high dynamic range" image. Your camera can offer help for this type of work or even for the complete job (usually at the price of not producing RAW image). Personally, I prefer to get lighting so that I can manage with a single shot.

Fill shadow detail is an example where a built-in flash near the axis (built-in or even circular flash) makes sense: the usual problem of lack of perspective because you do not see the shadows is exactly what you are looking for. you want extra flashes in order not to create shadows that compete with those of the main lighting.