diff --git a/docs/src/solvers/IntegralSolvers.md b/docs/src/solvers/IntegralSolvers.md
index 1b131b30..b56302d5 100644
--- a/docs/src/solvers/IntegralSolvers.md
+++ b/docs/src/solvers/IntegralSolvers.md
@@ -12,7 +12,7 @@ The following algorithms are available:
   - `CubaDivonne`: Divonne from Cuba.jl. Requires `using IntegralsCuba`. Works only for `>1`-dimensional integrations.
   - `CubaCuhre`: Cuhre from Cuba.jl. Requires `using IntegralsCuba`. Works only for `>1`-dimensional integrations.
   - `GaussLegendre`: Uses Gauss-Legendre quadrature with nodes and weights from FastGaussQuadrature.jl.
-  - `QuadratureFunction`: Accepts a user-defined function that returns nodes and weights.
+  - `QuadratureRule`: Accepts a user-defined function that returns nodes and weights.
 
 ```@docs
 QuadGKJL
diff --git a/src/Integrals.jl b/src/Integrals.jl
index 944c2176..9c73b40c 100644
--- a/src/Integrals.jl
+++ b/src/Integrals.jl
@@ -148,5 +148,5 @@ function __solvebp_call(prob::IntegralProblem, alg::VEGAS, sensealg, lb, ub, p;
     SciMLBase.build_solution(prob, alg, val, err, chi = chi, retcode = ReturnCode.Success)
 end
 
-export QuadGKJL, HCubatureJL, VEGAS, GaussLegendre, QuadratureFunction
+export QuadGKJL, HCubatureJL, VEGAS, GaussLegendre, QuadratureRule
 end # module
diff --git a/src/algorithms.jl b/src/algorithms.jl
index 371641b0..ca686beb 100644
--- a/src/algorithms.jl
+++ b/src/algorithms.jl
@@ -124,7 +124,7 @@ function GaussLegendre(; n = 250, subintervals = 1, nodes = nothing, weights = n
 end
 
 """
-    QuadratureFunction(q; n=250)
+    QuadratureRule(q; n=250)
 
 Algorithm to construct and evaluate a quadrature rule `q` of `n` points computed from the
 inputs as `x, w = q(n)`. It assumes the nodes and weights are for the standard interval
@@ -133,13 +133,13 @@ solved. The nodes `x` may be scalars in 1d or vectors in arbitrary dimensions, a
 weights `w` must be scalar. The algorithm computes the quadrature rule `sum(w .* f.(x))` and
 the caller must check that the result is converged with respect to `n`.
 """
-struct QuadratureFunction{Q} <: SciMLBase.AbstractIntegralAlgorithm
+struct QuadratureRule{Q} <: SciMLBase.AbstractIntegralAlgorithm
     q::Q
     n::Int
-    function QuadratureFunction(q::Q, n::Integer) where {Q}
+    function QuadratureRule(q::Q, n::Integer) where {Q}
         n > 0 ||
             throw(ArgumentError("Cannot use a nonpositive number of quadrature nodes."))
         return new{Q}(q, n)
     end
 end
-QuadratureFunction(q; n = 250) = QuadratureFunction(q, n)
+QuadratureRule(q; n = 250) = QuadratureRule(q, n)
diff --git a/src/quadrules.jl b/src/quadrules.jl
index adb9e427..982a291d 100644
--- a/src/quadrules.jl
+++ b/src/quadrules.jl
@@ -18,20 +18,19 @@ function evalrule(f, p, lb, ub, nodes, weights)
     return prod(scale) * I
 end
 
-function init_cacheval(alg::QuadratureFunction, ::IntegralProblem)
+function init_cacheval(alg::QuadratureRule, ::IntegralProblem)
     return alg.q(alg.n)
 end
 
-function Integrals.__solvebp_call(cache::IntegralCache, alg::QuadratureFunction,
+function Integrals.__solvebp_call(cache::IntegralCache, alg::QuadratureRule,
     sensealg, lb, ub, p;
     reltol = nothing, abstol = nothing,
     maxiters = nothing)
     prob = build_problem(cache)
     if isinplace(prob)
-        error("QuadratureFunction does not support inplace integrandss.")
+        error("QuadratureRule does not support inplace integrandss.")
     end
     @assert prob.batch == 0
-    @assert prob.nout == 1
 
     val = evalrule(cache.f, cache.p, lb, ub, cache.cacheval...)
 
diff --git a/test/quadrule_tests.jl b/test/quadrule_tests.jl
index 2c004cee..26869472 100644
--- a/test/quadrule_tests.jl
+++ b/test/quadrule_tests.jl
@@ -24,7 +24,7 @@ function trapz(n::Integer)
     return (x, w)
 end
 
-alg = QuadratureFunction(trapz, n = 1000)
+alg = QuadratureRule(trapz, n = 1000)
 
 lb = -1.2
 ub = 3.5
@@ -43,7 +43,7 @@ function trapz2(n)
     return [SVector(y, z) for (y, z) in Iterators.product(x, x)], w .* w'
 end
 
-alg = QuadratureFunction(trapz2, n = 100)
+alg = QuadratureRule(trapz2, n = 100)
 
 lb = SVector(-1.2, -1.0)
 ub = SVector(3.5, 3.7)
@@ -58,7 +58,7 @@ u = solve(prob, alg).u
 
 g = (x, p) -> p / (x^2 + p^2)
 
-alg = QuadratureFunction(gausslegendre, n = 1000)
+alg = QuadratureRule(gausslegendre, n = 1000)
 
 lb = -Inf
 ub = Inf
@@ -68,13 +68,28 @@ prob = IntegralProblem(g, lb, ub, p)
 
 @test solve(prob, alg).u≈pi rtol=1e-4
 
+# 1d with nout
+
+g2 = (x, p) -> [p[1] / (x^2 + p[1]^2), p[2] / (x^2 + p[2]^2)]
+
+alg = QuadratureRule(gausslegendre, n = 1000)
+
+lb = -Inf
+ub = Inf
+p = (1.0, 1.3)
+
+prob = IntegralProblem(g2, lb, ub, p)
+
+@test solve(prob, alg).u≈[pi,pi] rtol=1e-4
+
+
 #= derivative tests
 
 using Zygote
 
 function testf(lb, ub, p, f = f)
     prob = IntegralProblem(f, lb, ub, p)
-    solve(prob, QuadratureFunction(trapz, n=200))[1]
+    solve(prob, QuadratureRule(trapz, n=200))[1]
 end
 
 lb = -1.2