The phrase "a different task with" is correct and usable in written English.
It can be used when referring to a distinct or alternative task that involves a specific element or aspect.
Example: "I have been assigned a different task with a tighter deadline that requires immediate attention."
Alternatives: "an alternative task involving" or "a separate task related to".
A definite investigation of a spatial bias in our patients' deficit would require a different task design with a systematic mapping of the visual field with smaller stimulus displacements.
Like their modern counterparts, they may have lived in the equivalent of microbial cities that hosted thousands of kinds of bacteria, each specialised for a different task and communicating with the others via chemical signals.
"We knew the crowd were going to get behind the team second half, and we had a different task to contend with.
Speaking other languages at native level is an entirely different task with different rewards to just being a polyglot.
At the Hudson River Museum, Mr. Morton was faced with a different task.
Immediately afterward, half the participants were encouraged to deliberate on who was trustworthy, while the others were told to distract themselves with a different task.
Every week I am assisting with a different task, and it is exciting to watch all of our research plots progress.
Michael J. Foreman of the Navy began with a different task: replacing a circuit breaker that routes power to one of the four gyroscopes that help maintain the orbiting laboratory's attitude.
The students were divided into more than a dozen groups, each focused on a different task: attracting news media attention with catchy demonstrations, dogging the tracks of lobbyists for oil companies and the Organization of the Petroleum Exporting Countries, talking with American negotiators, who were seen as seeking loopholes, or delegates from countries that had strong environmental policies.
