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=============================================
Integration and ODEs (:mod:`scipy.integrate`)
=============================================

.. currentmodule:: scipy.integrate

Integrating functions, given function object
============================================

.. autosummary::
   :toctree: generated/

   quad          -- General purpose integration
   dblquad       -- General purpose double integration
   tplquad       -- General purpose triple integration
   nquad         -- General purpose n-dimensional integration
   fixed_quad    -- Integrate func(x) using Gaussian quadrature of order n
   quadrature    -- Integrate with given tolerance using Gaussian quadrature
   romberg       -- Integrate func using Romberg integration
   quad_explain  -- Print information for use of quad
   newton_cotes  -- Weights and error coefficient for Newton-Cotes integration
   IntegrationWarning -- Warning on issues during integration

Integrating functions, given fixed samples
==========================================

.. autosummary::
   :toctree: generated/

   trapz         -- Use trapezoidal rule to compute integral.
   cumtrapz      -- Use trapezoidal rule to cumulatively compute integral.
   simps         -- Use Simpson's rule to compute integral from samples.
   romb          -- Use Romberg Integration to compute integral from
                 -- (2**k + 1) evenly-spaced samples.

.. seealso::

   :mod:`scipy.special` for orthogonal polynomials (special) for Gaussian
   quadrature roots and weights for other weighting factors and regions.

Integrators of ODE systems
==========================

.. autosummary::
   :toctree: generated/

   odeint        -- General integration of ordinary differential equations.
   ode           -- Integrate ODE using VODE and ZVODE routines.
   complex_ode   -- Convert a complex-valued ODE to real-valued and integrate.
   solve_bvp     -- Solve a boundary value problem for a system of ODEs.
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