The monad rolled around the woods, careful not to fall into the river.
La monado ruliĝis tra la arboj, atentanta (por ke) ne fali en la riveron.
Adjective, careful relates to the monad.
The human was careful not to awaken the baby.
La homo atentis ne veki la bebon.
La homo atentis por ne veki la bebon.
Adjective too, quite clear. However be+adjective can be translated as verb in Esperanto. To stress the carefulness por might be injected.
She was keen to win his affections.
Ŝi deziris gajni lian amon.
Ŝi estis fervora por akiri lian kor(inklin)on.
Adjective too, even more clear. In Esperanto be+adjective can become verb too.
