The part of the sentence "engaged with a task" is correct and usable in written English.
You can use it to describe someone who is working on a task and is focused on it. For example, "John was completely engaged with the task at hand, working diligently to finish it on time."
In a well-known study looking at happiness in teenagers, the psychologist Mihaly Csikszentmihalyi found that his subjects were happiest when they were in what he calls a "flow state," where one is fully engaged with an activity or task.
Animals were engaged with a variety of psychologically enriching tasks.
Physical manipulatives are thought to provide several unique affordances, the most obvious being the opportunity to physically engage with a learning task.
Only when we have a qualitative description of how students are likely to engage with a particular task can we begin to develop more quantitative instruments to assess its success (e.g., Dreyfus et al., 2013a).
The results from the current study suggest that tDCS is more effective when participants have to fully engage with a difficult task, or when they find it difficult to perform.
An analysis of the response time data suggested that subjects were engaged with the task and spent a reasonable amount of time determining which photos were authentic.
A task engagement is being engaged with the tasks and accomplishing it without being stopped by inability to convey meaning because of language problems.
The dull fact is, we spend most of our time engaged with the task at hand – rehearsing, writing, booking tours.
With it, Bush, the former governor of Florida, was asking his volunteers to go "all in" in support of his candidacy, and suggesting by association that, in contrast with his previous flirtations with running for the White House, he would be fully engaged with the task this time, too.
