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Modern cloud databases adopt a storage-disaggregation architecture that separates the management of computation and storage. A major bottleneck in such an architecture is the network connecting the computation and storage layers. Two solutions have been explored to mitigate the bottleneck: caching and computation pushdown. While both techniques can significantly reduce network traffic, existing DBMSs consider them as orthogonal techniques and support only one or the other, leaving potential performance benefits unexploited. In this paper we present FlexPushdownDB (FPDB), an OLAP cloud DBMS prototype that supports fine-grained hybrid query execution to combine the benefits of caching and computation pushdown in a storage-disaggregation architecture. We build a hybrid query executor based on a new concept called separable operators to combine the data from the cache and results from the pushdown processing. We also propose a novel Weighted-LFU cache replacement policy that takes into account the cost of pushdown computation. Our experimental evaluation on the Star Schema Benchmark shows that the hybrid execution outperforms both the conventional caching- only architecture and pushdown-only architecture by 2.2×. In the hybrid architecture, our experiments show that Weighted-LFU can outperform the baseline LFU by 37%.