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Pick-and-place is an important manipulation task in domestic or manufacturing applications. There exist many works focusing on grasp detection with high picking success rate but lacking consideration of downstream manipulation tasks (e.g., placing). Although some research works proposed methods to incorporate task conditions into grasp selection, most of them are data-driven and are therefore hard to adapt to arbitrary operating environments. Observing this challenge, we propose a general task-oriented pick-place framework that treats the target task and operating environment as placing constraints into grasping optimization. Combined with existing grasp detectors, our framework is able to generate feasible grasps for different downstream tasks and adapt to environmental changes without time-consuming re-training processes. Moreover, the framework can accept different definitions of placing constraints, so it is easy to integrate with other modules. Experiments in the simulator and real-world on multiple pick-place tasks are conducted to evaluate the performance of our framework. The result shows that our framework achieves a high and robust task success rate on a wide variety of the pick-place tasks.