I'm supposed to be able to queue a build with the Rest API
POST https://dev.azure.com/{organization}/{project}/_apis/build/builds?api-version=5.0-preview.5
I just can't figure out what should be included in the request body and how to assemble it.
I'm using powershell and modifying a script i've used to query DevOps that works just fine:
function Queue-Build
{
    param (
        [string] $BuildUri,
        [Hashtable] $Headers
    )
    # Can't figure out how to assemble body    
    $build = Invoke-RestMethod -Uri $BuildUri -Headers $Headers -Method Post -Body $body
    return $build
}
function Set-AuthHeaders
{
    [CmdletBinding()]
    param (
        [string] $UserName = "",
        [string] $AccessToken
    )
    $basicAuth = [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes(("{0}:{1}" -f $UserName,$AccessToken)))
    return @{ Authorization = "Basic $basicAuth" }
}
# Azure DevOps settings
$AccessToken = 'my_access_token'
$vstsProjectUri = 'https://org.visualstudio.com/project'
$vstsApiVersion = "5.0-preview.5"
$headers = Set-AuthHeaders -AccessToken $AccessToken
# Queue a new build
$buildDefinitionUri = "$vstsProjectUri/_apis/build/builds?api-version=$vstsApiVersion"
$buildQueueResult = Queue-Build -BuildUri $buildDefinitionUri -Headers $headers
$buildQueueResult