  We produce the first low to mid frequency radio simulation that incorporates
both traditional extragalactic radio sources as well as synchrotron cosmic web
emission. The FIlaments \& GAlactic RadiO (FIGARO) simulation includes ten
unique \SI{4x4}{\degree} fields, incorporating active galactic nucleii (AGNs),
star forming galaxies (SFGs) and synchrotron cosmic web emission out to a
redshift of $z = 0.8$ and over the frequency range 100-1400 MHz. To do this,
the simulation brings together a recent $100^3$ Mpc$^3$ magneto-hydrodynamic
simulation (Vazza et al., 2019), calibrated to match observed radio relic
population statistics, alongside updated `T-RECS' code for simulating
extragalactic radio sources (Bonaldi et al., 2019). Uniquely, the AGNs and SFGs
are populated and positioned in accordance with the underlying matter density
of the cosmological simulation. In this way, the simulation provides an
accurate understanding of the apparent morphology, angular scales, and
brightness of the cosmic web as well as -- crucially -- the clustering
properties of the cosmic web with respect to the embedded extragalactic radio
population. We find that the synchrotron cosmic web does not closely trace the
underlying mass distribution of the cosmic web, but is instead dominated by
shocked shells of emission surrounding dark matter halos and resembles a large,
undetected population of radio relics. We also show that, with accurate
kernels, the cosmic web radio emission is clearly detectable by
cross-correlation techniques and this signal is separable from the embedded
extragalactic radio population. We offer the simulation as a public resource
towards the development of techniques for detecting and measuring the
synchrotron cosmic web.
