Users today expect more security from services that handle their data. In addition to traditional data privacy and integrity requirements, they expect transparency, i.e., that the service's processing of the data is verifiable by users and trusted auditors. Our goal is to build a multi-user system that provides data privacy, integrity, and transparency for a large number of operations, while achieving practical performance. To this end, we first identify the limitations of existing approaches that use authenticated data structures. We find that they fall into two categories: 1) those that hide each user's data from other users, but have a limited range of verifiable operations (e.g., CONIKS, Merkle2, and Proofs of Liabilities), and 2) those that support a wide range of verifiable operations, but make all data publicly visible (e.g., IntegriDB and FalconDB). We then present TAP to address the above limitations. The key component of TAP is a novel tree data structure that supports efficient result verification, and relies on independent audits that use zero-knowledge range proofs to show that the tree is constructed correctly without revealing user data. TAP supports a broad range of verifiable operations, including quantiles and sample standard deviations. We conduct a comprehensive evaluation of TAP, and compare it against two state-of-the-art baselines, namely IntegriDB and Merkle2, showing that the system is practical at scale.